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Classical and Quantum Mechanical Motion in Magnetic Fields: We study the motion of a particle in a particular magnetic field
configuration both classically and quantum mechanically. For flux-free radially
symmetric magnetic fields defined on circular regions, we establish that
particle escape speeds depend, classically, on a gauge-fixed magnetic vector
potential, and demonstrate some trajectories associated with this special type
of magnetic field. Then we show that some of the geometric features of the
classical trajectory (perpendicular exit from the field region, trapped and
escape behavior) are reproduced quantum mechanically using a numerical method
that extends the norm-preserving Crank-Nicolson method to problems involving
magnetic fields. While there are similarities between the classical trajectory
and the position expectation value of the quantum mechanical solution, there
are also differences, and we demonstrate some of these.
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quant-ph
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$\mathcal{PT}$ phase transition in open quantum systems with Lindblad
dynamics: We investigate parity-time ($\mathcal{PT}$) phase transitions in open quantum
systems and discuss a criterion of Liouvillian $\mathcal{PT}$ symmetry proposed
recently by Huber \textit{et al}. [J. Huber \textit{et al}., SciPost Phys.
$\textbf{9}$, 52 (2020)]. Using the third quantization, which is a general
method to solve the Lindblad equation for open quadratic systems, we show, with
a proposed criterion of $\mathcal{PT}$ symmetry, that the eigenvalue structure
of the Liouvillian clearly changes at the $\mathcal{PT}$ symmetry breaking
point for an open 2-spin model with exactly balanced gain and loss if the total
spin is large. In particular, in a $\mathcal{PT}$ unbroken phase, some
eigenvalues are pure imaginary numbers while in a $\mathcal{PT}$ broken phase,
all the eigenvalues are real. From this result, it is analytically shown for an
open quantum system including quantum jumps that the dynamics in the long time
limit changes from an oscillatory to an overdamped behavior at the proposed
$\mathcal{PT}$ symmetry breaking point. Furthermore, we show a direct relation
between the criterion of Huber \textit{et al}. of Liouvillian $\mathcal{PT}$
symmetry and the dynamics of the physical quantities for quadratic bosonic
systems. Our results support the validity of the proposed criterion of
Liouvillian $\mathcal{PT}$ symmetry.
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quant-ph
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Skein Theory and Topological Quantum Registers: Braiding Matrices and
Topological Entanglement Entropy of Non-Abelian Quantum Hall States: We study topological properties of quasi-particle states in the non-Abelian
quantum Hall states. We apply a skein-theoretic method to the Read--Rezayi
state whose effective theory is the SU(2)_K Chern--Simons theory. As a
generalization of the Pfaffian (K=2) and the Fibonacci (K=3) anyon states, we
compute the braiding matrices of quasi-particle states with arbitrary spins.
Furthermore we propose a method to compute the entanglement entropy
skein-theoretically. We find that the entanglement entropy has a nontrivial
contribution called the topological entanglement entropy which depends on the
quantum dimension of non-Abelian quasi-particle intertwining two subsystems.
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quant-ph
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Quantum Open System Theory: Bipartite Aspects: We demonstrate in straightforward calculations that even under ideally weak
noise the relaxation of bipartite open quantum systems contains elements not
previously encountered in quantum noise physics. While additivity of decay
rates is known to be generic for decoherence of a single system, we demonstrate
that it breaks down for bipartite coherence of even the simplest composite
systems.
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quant-ph
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Enhancing self-discharging process with disordered quantum batteries: One of the most important devices emerging from quantum technology are
quantum batteries. However, self-discharging, the process of charge wasting of
quantum batteries due to decoherence phenomenon, limits their performance,
measured by the concept of ergotropy and half-life time of the quantum battery.
The effects of local field fluctuation, introduced by disorder term in
Hamiltonian of the system, on the performance of the quantum batteries is
investigated in this paper. The results reveal that the disorder term could
compensate disruptive effects of the decoherence, i.e. self-discharging, and
hence improve the performance of the quantum battery via "incoherent gain of
ergotropy" procedure. Adjusting the strength of disorder parameter to a proper
value and choosing a suitable initial state of quantum battery, the amount of
free ergotropy, defined with respect to free Hamiltonian, could exceed the
amount of initial stored ergotropy. In addition harnessing the degree of
disorder parameter could help to enhance the half-life time of the quantum
battery. This study opens perspective to further investigation of the
performance of quantum batteries that explore disorder and many-body effects.
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quant-ph
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A blueprint for demonstrating quantum supremacy with superconducting
qubits: Fundamental questions in chemistry and physics may never be answered due to
the exponential complexity of the underlying quantum phenomena. A desire to
overcome this challenge has sparked a new industry of quantum technologies with
the promise that engineered quantum systems can address these hard problems. A
key step towards demonstrating such a system will be performing a computation
beyond the capabilities of any classical computer, achieving so-called quantum
supremacy. Here, using 9 superconducting qubits, we demonstrate an immediate
path towards quantum supremacy. By individually tuning the qubit parameters, we
are able to generate thousands of unique Hamiltonian evolutions and probe the
output probabilities. The measured probabilities obey a universal distribution,
consistent with uniformly sampling the full Hilbert-space. As the number of
qubits in the algorithm is varied, the system continues to explore the
exponentially growing number of states. Combining these large datasets with
techniques from machine learning allows us to construct a model which
accurately predicts the measured probabilities. We demonstrate an application
of these algorithms by systematically increasing the disorder and observing a
transition from delocalized states to localized states. By extending these
results to a system of 50 qubits, we hope to address scientific questions that
are beyond the capabilities of any classical computer.
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quant-ph
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Spontaneously emitted X-rays: an experimental signature of the dynamical
reduction models: We present the idea of searching for X-rays as a signature of the mechanism
inducing the spontaneous collapse of the wave function. Such a signal is
predicted by the continuous spontaneous localization theories, which are
solving the "measurement problem" by modifying the Schrodinger equation. We
will show some encouraging preliminary results and discuss future plans and
strategy.
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quant-ph
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Quantum Template Matching: We consider the quantum analogue of the pattern matching problem, which
consists of classifying a given unknown system according to certain predefined
pattern classes. We address the problem of quantum template matching in which
each pattern class ${\cal C}_i$ is represented by a known quantum state $\hat
g_i$ called a template state, and our task is to find a template which
optimally matches a given unknown quantum state $\hat f$. We set up a precise
formulation of this problem in terms of the optimal strategy for an associated
quantum Bayesian inference problem. We then investigate various examples of
quantum template matching for qubit systems, considering the effect of allowing
a finite number of copies of the input state $\hat f$. We compare quantum
optimal matching strategies and semiclassical strategies and demonstrate an
entanglement assisted enhancement of performance in the general quantum optimal
strategy.
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quant-ph
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Generalized plasma-like permittivity and thermal Casimir force between
real metals: The physical reasons why the Drude dielectric function is not compatible with
the Lifshitz formula, as opposed to the generalized plasma-like permittivity,
are presented. Essentially, the problem is connected with the finite size of
metal plates. It is shown that the Lifshitz theory combined with the
generalized plasma-like permittivity is thermodynamically consistent.
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quant-ph
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Efficient and robust adiabatic universal quantum computation using
STIRAP on a qubit chain: It is shown that efficient and robust universal quantum computation is
possible using the stimulated Raman adiabatic passage with a qubit chain as a
pointer register.
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quant-ph
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Satisfying the Einstein-Podolsky-Rosen criterion with massive particles: In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of
quantum mechanics by devising a quantum state of two massive particles with
maximally correlated space and momentum coordinates. The EPR criterion
qualifies such continuous-variable entangled states, where a measurement of one
subsystem seemingly allows for a prediction of the second subsystem beyond the
Heisenberg uncertainty relation. Up to now, continuous-variable EPR
correlations have only been created with photons, while the demonstration of
such strongly correlated states with massive particles is still outstanding.
Here, we report on the creation of an EPR-correlated two-mode squeezed state in
an ultracold atomic ensemble. The state shows an EPR entanglement parameter of
0.18(3), which is 2.4 standard deviations below the threshold 1/4 of the EPR
criterion. We also present a full tomographic reconstruction of the underlying
many-particle quantum state. The state presents a resource for tests of quantum
nonlocality and a wide variety of applications in the field of
continuous-variable quantum information and metrology.
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quant-ph
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Which Kind of Two-Particle States Can Be Teleported through a
Three-Particle Quantum Channel?: The use of a three-particle quantum channel to teleport entangled states
through a slight modification of the standard teleportation procedure is
studied. It is shown that it is not possible to perform successful
teleportation of an arbitrary and unknown two-particle entangled state,
following our version of the standard teleportation procedure. On the contrary,
it is shown which, and in how many different ways, particular classes of
two-particle states can be teleported.
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quant-ph
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Efficient Deterministic Preparation of Quantum States Using Decision
Diagrams: Loading classical data into quantum registers is one of the most important
primitives of quantum computing. While the complexity of preparing a generic
quantum state is exponential in the number of qubits, in many practical tasks
the state to prepare has a certain structure that allows for faster
preparation. In this paper, we consider quantum states that can be efficiently
represented by (reduced) decision diagrams, a versatile data structure for the
representation and analysis of Boolean functions. We design an algorithm that
utilises the structure of decision diagrams to prepare their associated quantum
states. Our algorithm has a circuit complexity that is linear in the number of
paths in the decision diagram. Numerical experiments show that our algorithm
reduces the circuit complexity by up to 31.85% compared to the state-of-the-art
algorithm, when preparing generic $n$-qubit states with different degrees of
non-zero amplitudes. Additionally, for states with sparse decision diagrams,
including the initial state of the quantum Byzantine agreement protocol, our
algorithm reduces the number of CNOTs by 86.61% $\sim$ 99.9%.
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quant-ph
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Fabrication of Magnetic Charge From Excited States of H-atom: It is shown that the excited states of hydrogen atom in a uniform electric
field (Stark States) posess magnetic charge whose magnitude is given by a
Dirac-Saha type relation: $$ {eg\over \hbar c} = \sqrt 3 n $$ An experiment is
proposed to fabricate such states and to detect their magnetic charge.
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quant-ph
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Overturning negative construal of quantum superposition: Construal of observable facts or events, that is, the manner in which we
understand reality, is based not only on mathematical formulas of a theory
suggested as a reasonable explanation for physical phenomena (like general
relativity or quantum mechanics), but also on a mathematical model of reasoning
used to analyze and appraise statements regarding the objective world (for
example, logic of one type or the other). Hence, every time that a certain
construal of reality encounters a problem, there is a choice between a
modification to the mathematical formalism of the physical theory and a change
in the model of reasoning. A case in point is negative construal of quantum
superposition causing the problem of definite outcomes. To be sure, according
to the said construal, it is not the case that a system being in a
superposition of states is exclusively in one of the states constituting the
superposition, which in turn implies that macroscopically differing outcomes of
observation may appear all at once. The usual approach to the problem of
definite outcomes is to modify the quantum mathematical formalism by adding to
it some extra postulates (for instance, the postulate of wave function
collapse). However, since none of the extra postulates proposed so far has
gained broad acceptance, one may try another avenue to resolve the problem,
namely, to replace logic with an alternative mathematical model of reasoning.
This possibility is studied in the present paper.
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quant-ph
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Postulating the Unicity of the Macroscopic Physical World: We argue that a clear view on quantum mechanics is obtained by considering
that the unicity of the macroscopic world is a fundamental postulate of
physics, rather than an issue that must be mathematically justified or
demonstrated. This postulate allows a framework in which quantum mechanics can
be constructed, in a complete mathematically consistent way. This is made
possible by using general operator algebras to extend the mathematical
description of the physical world towards macroscopic systems. Such an approach
goes beyond the usual type I operator algebras used in standard textbook
quantum mechanics. This avoids a major pitfall, which is the temptation to make
the usual type I formalism 'universal'. This may also provide a meta-framework
for both classical and quantum physics, shedding a new light on ancient
conceptual antagonisms, and clarifying the status of quantum objects. Beyond
exploring remote corners of quantum physics, we expect these ideas to be
helpful to better understand and develop quantum technologies.
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quant-ph
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Comment on "Non-representative Quantum Mechanical Weak Values": Svensson [Found. Phys. 45, 1645 (2015)] argued that the concept of the weak
value of an observable of a pre- and post-selected quantum system cannot be
applied when the expectation value of the observable in the initial state
vanishes. Svensson's argument is analyzed and shown to be inconsistent using
several examples.
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quant-ph
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Dynamical identification of open quantum systems: I propose a quantum trajectories approach to parametric identification of the
effective Hamiltonian for a Markovian open quantum system, and discuss an
application motivated by recent experiments in cavity quantum electrodynamics.
This example illustrates a strategy for quantum parameter estimation that
efficiently utilizes the information carried by correlations between
measurements distributed in time.
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quant-ph
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Qubitization of Bosons: A binary mapping from Fock space of bosonic state to qubits is given. Based
on the binary mapping, we construte an algorithm of qubitization of bosons with
complexity O(log(N)). As an example, the algorithm of qubitization of bosons in
matrix product state to simulate real time dynamics of Yukawa coupling is
realized. The calculation error bar is estimated by random sampling method.
This proposal may be achieved in superconductivity noisy intermediate--scale
quantum computer not far future.
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quant-ph
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Optimal choice of state tomography quorum formed by projection operators: A minimal set of measurement operators for quantum state tomography has in
the non-degenerate case ideally eigenbases which are mutually unbiased. This is
different for the degenerate case. Here, we consider the situation where the
measurement operators are projections on individual pure quantum states. This
corresponds to maximal degeneracy. We present numerically optimized sets of
projectors and find that they significantly outperform those which are taken
from a set of mutually unbiased bases.
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quant-ph
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A weak-value model for virtual particles supplying the electric current
in graphene: the minimal conductivity and the Schwinger mechanism: We propose a model for the electric current in graphene in which electric
carriers are supplied by virtual particles allowed by the uncertainty
relations. The process to make a virtual particle real is described by a weak
value of a group velocity: the velocity is requisite for the electric field to
give the virtual particle the appropriate changes of both energy and momentum.
With the weak value, we approximately estimate the electric current,
considering the ballistic transport of the electric carriers. The current shows
the quasi-Ohimic with the minimal conductivity of the order of e^2/h per
channel. Crossing a certain ballistic time scale, it is brought to obey the
Schwinger mechanism.
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quant-ph
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Exact bistability and time pseudo-crystallization of driven-dissipative
fermionic lattices: The existence of bistability in quantum optical systems remains a intensely
debated open question beyond the mean-field approximation. Quantum fluctuations
are finite-size corrections to the mean-field approximation used because the
full exact solution is unobtainable. Usually, quantum fluctuations destroy the
bistability present on the mean-field level. Here, by identifying and using
exact modulated semi-local dynamical symmetries in a certain quantum optical
models of driven-dissipative fermionic chains we exactly prove bistability in
precisely the quantum fluctuations. Surprisingly, rather than destroying
bistability, the quantum fluctuations themselves exhibit bistability, even
though it is absent on the mean-field level for our systems. Moreover, the
models studied acquire additional thermodynamic dynamical symmetries that imply
persistent periodic oscillations in the quantum fluctuations, constituting
pseudo-variants of boundary time crystals. Physically, these emergent operators
correspond to finite-frequency and finite-momentum semi-local Goldstone modes.
Our work therefore provides to the best of our knowledge the first example of a
provably bistable quantum optical system.
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quant-ph
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Emerging dynamics arising from coarse-grained quantum systems: The purpose of physics is to describe nature from elementary particles all
the way up to cosmological objects like cluster of galaxies and black holes.
Although a unified description for all this spectrum of events is desirable,
this would be highly impractical. To not get lost in unnecessary details,
effective descriptions are mandatory. Here we analyze the dynamics that may
emerge from a full quantum description when one does not have access to all the
degrees of freedom of a system. More concretely, we describe the properties of
the dynamics that arise from quantum mechanics if one has access only to a
coarse-grained description of the system. We obtain that the effective maps are
not necessarily of Kraus form, due to correlations between accessible and
nonaccessible degrees of freedom, and that the distance between two effective
states may increase under the action of the effective map. We expect our
framework to be useful for addressing questions such as the thermalization of
closed quantum systems, as well as the description of measurements in quantum
mechanics.
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quant-ph
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Routes towards the experimental observation of the large fluctuations
due to chaos assisted tunneling effects with cold atoms: In the presence of a complex classical dynamics associated with a mixed phase
space, a quantum wave function can tunnel between two stable islands through
the chaotic sea, an effect that has no classical counterpart. This phenomenon,
referred to as chaos assisted tunneling, is characterized by large fluctuations
of the tunneling rate when a parameter is varied. To date the full extent of
this effect as well as the associated statistical distribution have never been
observed in a quantum system. Here we analyze the possibility of characterizing
these effects accurately in a cold atom experiment. Using realistic values of
the parameters of an experimental setup, we examine through analytical
estimates and extensive numerical simulations a specific system that can be
implemented with cold atoms, the atomic modulated pendulum. We assess the
efficiency of three possible routes to observe in detail chaos assisted
tunneling properties. Our main conclusion is that due to the fragility of the
symmetry between positive and negative momenta as a function of quasimomentum,
it is very challenging to use tunneling between classical islands centered on
fixed points with opposite momentum. We show that it is more promising to use
islands symmetric in position space, and characterize the regime where it could
be done. The proposed experiment could be realized with current
state-of-the-art technology.
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quant-ph
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Discrete time Dirac quantum walk in 3+1 dimensions: In this paper we consider quantum walks whose evolution converges to the
Dirac equation one in the limit of small wave-vectors. We show exact Fast
Fourier implementation of the Dirac quantum walks in one, two and three space
dimensions. The behaviour of particle states, defined as states smoothly peaked
in some wave-vector eigenstate of the walk, is described by an approximated
dispersive differential equation that for small wave-vectors gives the usual
Dirac particle and antiparticle kinematics. The accuracy of the approximation
is provided in terms of a lower bound on the fidelity between the exactly
evolved state and the approximated one. The jittering of the position operator
expectation value for states having both a particle and an antiparticle
component is analytically derived and observed in the numerical
implementations.
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quant-ph
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Time-invariant Discord: High Temperature Limit and Initial Environmental
Correlations: We present a thorough investigation of the phenomena of frozen and
time-invariant quantum discord for two-qubit systems independently interacting
with local reservoirs. Our work takes into account several significant effects
present in decoherence models, which have not been yet explored in the context
of time-invariant quantum discord, but which in fact must be typically
considered in almost all realistic models. Firstly, we study the combined
influence of dephasing, dissipation and heating reservoirs at finite
temperature. Contrarily to previous claims in the literature, we show the
existence of time-invariant discord at high temperature limit in the weak
coupling regime, and also examine the effect of thermal photons on the
dynamical behaviour of frozen discord. Secondly, we explore the consequences of
having initial correlations between the dephasing reservoirs. We demonstrate in
detail how the time-invariant discord is modified depending on the relevant
system parameters such as the strength of the initial amount of entanglement
between the reservoirs.
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quant-ph
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Heisenberg chains cannot mirror a state: Faithful exchange of quantum information can in future become a key part of
many computational algorithms. Some Authors suggest to use chains of mutually
coupled spins as channels for quantum communication. One can divide these
proposals into the groups of assisted protocols, which require some additional
action from the users, and natural ones, based on the concept of state
mirroring. We show that mirror is fundamentally not the feature chains of
spins-1/2 coupled by the Heisenberg interaction, but without local magnetic
fields. This fact has certain consequences in terms of the natural state
transfer.
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quant-ph
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A quantum memory at telecom wavelengths: Nanofabricated mechanical resonators are gaining significant momentum among
potential quantum technologies due to their unique design freedom and
independence from naturally occurring resonances. With their functionality
being widely detached from material choice, they constitute ideal tools to be
used as transducers, i.e. intermediaries between different quantum systems, and
as memory elements in conjunction with quantum communication and computing
devices. Their capability to host ultra-long lived phonon modes is
particularity attractive for non-classical information storage, both for future
quantum technologies as well as for fundamental tests of physics. Here we
demonstrate such a mechanical quantum memory with an energy decay time of
$T_1\approx2$ ms, which is controlled through an optical interface engineered
to natively operate at telecom wavelengths. We further investigate the
coherence of the memory, equivalent to the dephasing $T_2^*$ for qubits, which
exhibits a power dependent value between 15 and 112 $\mu$s. This demonstration
is enabled by a novel optical scheme to create a superposition state of
$\rvert{0}\rangle+\rvert{1}\rangle$ mechanical excitations, with an arbitrary
ratio between the vacuum and single phonon components.
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quant-ph
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Experimental High-Dimensional Entanglement by Path Identity: Versatile and high-brightness sources of high-dimensional entangled photon
pairs are important for emerging quantum technologies such as secure quantum
communication. Here, we experimentally demonstrate a new scalable method to
create photon pairs carrying orbital angular momentum that are entangled in
arbitrarily high dimensions. Our method relies on indistinguishable photon
pairs created coherently in different sources. We demonstrate the creation of
three-dimensionally entangled states and show how to incrementally increase the
dimensionality of entanglement. The generated states retain their quality even
in higher dimensions. In addition, the modular structure of our approach allows
for generalization to various degrees of freedom and even implementation in
integrated compact devices. We therefore expect that future quantum
technologies and fundamental tests of nature in higher dimensions will benefit
from this novel approach.
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quant-ph
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Computation in generalised probabilistic theories: From the existence of an efficient quantum algorithm for factoring, it is
likely that quantum computation is intrinsically more powerful than classical
computation. At present, the best upper bound known for the power of quantum
computation is that BQP is in AWPP. This work investigates limits on
computational power that are imposed by physical principles. To this end, we
define a circuit-based model of computation in a class of operationally-defined
theories more general than quantum theory, and ask: what is the minimal set of
physical assumptions under which the above inclusion still holds? We show that
given only an assumption of tomographic locality (roughly, that multipartite
states can be characterised by local measurements), efficient computations are
contained in AWPP. This inclusion still holds even without assuming a basic
notion of causality (where the notion is, roughly, that probabilities for
outcomes cannot depend on future measurement choices). Following Aaronson, we
extend the computational model by allowing post-selection on measurement
outcomes. Aaronson showed that the corresponding quantum complexity class is
equal to PP. Given only the assumption of tomographic locality, the inclusion
in PP still holds for post-selected computation in general theories. Thus in a
world with post-selection, quantum theory is optimal for computation in the
space of all general theories. We then consider if relativised complexity
results can be obtained for general theories. It is not clear how to define a
sensible notion of an oracle in the general framework that reduces to the
standard notion in the quantum case. Nevertheless, it is possible to define
computation relative to a `classical oracle'. Then, we show there exists a
classical oracle relative to which efficient computation in any theory
satisfying the causality assumption and tomographic locality does not include
NP.
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quant-ph
|
Qubit Sensing: A New Attack Model for Multi-programming Quantum
Computing: Noisy quantum computers suffer from readout or measurement error. It is a
classical bit-flip error due to which state "1" is read out as "0" and
vice-versa. The probability of readout error shows a state dependence i.e.,
flipping probability of state "1" may differ from flipping probability of state
"0". Moreover, the probability shows correlation across qubits. These
state-dependent and correlated error probability introduces a signature of
victim outputs on adversary output when two programs are run simultaneously on
the same quantum computer. This can be exploited to sense victim output which
may contain sensitive information. In this paper, we systematically show that
such readout error-dependent signatures exist and that an adversary can use
such signature to infer a user output. We experimentally demonstrate the attack
(inference) on 3 public IBM quantum computers. Using Jensen-Shannon Distance
(JSD) a measure for statistical inference, we show that our approach identifies
victim output with an accuracy of 96% on real hardware. We also present
randomized output flipping as a lightweight yet effective countermeasure to
thwart such information leakage attacks. Our analysis shows the countermeasure
incurs a minor penalty of 0.05% in terms of fidelity.
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quant-ph
|
Comment on ``Kepler problem in Dirac theory for a particle with
position-dependent mass'': Based on easy-to-follow considerations it is not difficult to be vehemently
opposed not only the solutions found in that paper but also the conclusions
manifested there.
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quant-ph
|
Lower Bounds on the Communication Complexity of Binary Local Quantum
Measurement Simulation: We consider the problem of the classical simulation of quantum measurements
in the scenario of communication complexity. Regev and Toner (2007) have
presented a 2-bit protocol which simulates one particular correlation function
arising from binary projective quantum measurements on arbitrary state, and in
particular does not preserve local averages. The question of simulating other
correlation functions using a protocol with bounded communication, or
preserving local averages, has been posed as an open one. Within this paper we
resolve it in the negative: we show that any such protocol must have unbounded
communication for some subset of executions. In particular, we show that for
any protocol, there exist inputs for which the random variable describing the
number of communicated bits has arbitrarily large variance.
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quant-ph
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Theory of strong down-conversion in multi-mode cavity and circuit QED: We revisit the superstrong coupling regime of multi-mode cavity quantum
electrodynamics (QED), defined to occur when the frequency of vacuum Rabi
oscillations between the qubit and the nearest cavity mode exceeds the cavity's
free spectral range. A novel prediction is made that the cavity's linear
spectrum, measured in the vanishing power limit, can acquire an intricate fine
structure associated with the qubit-induced cascades of coherent single-photon
down-conversion processes. This many-body effect is hard to capture by a
brute-force numerics and it is sensitive to the light-matter coupling
parameters both in the infra-red and the ultra-violet limits. We focused at the
example case of a superconducting fluxonium qubit coupled to a long
transmission line section. The conversion rate in such a circuit QED setup can
readily exceed a few MHz, which is plenty to overcome the usual decoherence
processes. Analytical calculations were made possible by an unconventional
gauge choice, in which the qubit circuit interacts with radiation via the
flux/charge variable in the low-/high-frequency limits, respectively. Our
prediction of the fine spectral structure lays the foundation for the "strong
down-conversion" regime in quantum optics, in which a single photon excited in
a non-linear medium spontaneously down-converts faster than it is absorbed.
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quant-ph
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Towards a unified picture of polarization transfer -- pulsed DNP and
chemically equivalent PHIP: Nuclear spin hyperpolarization techniques, such as dynamic nuclear
polarization (DNP) and parahydrogen-induced polarization (PHIP), have
revolutionized nuclear magnetic resonance and magnetic resonance imaging. In
these methods, a readily available source of high spin order, either electron
spins in DNP or singlet states in hydrogen for PHIP, is brought into close
proximity with nuclear spin targets, enabling efficient transfer of spin order
under external quantum control. Despite vast disparities in energy scales and
interaction mechanisms between electron spins in DNP and nuclear singlet states
in PHIP, a pseudo-spin formalism allows us to establish an intriguing
equivalence. As a result, the important low-field polarization transfer regime
of PHIP can be mapped onto an analogous system equivalent to pulsed-DNP. This
establishes a correspondence between key polarization transfer sequences in
PHIP and DNP, facilitating the transfer of sequence development concepts. This
promises fresh insights and significant cross-pollination between DNP and PHIP
polarization sequence developers.
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quant-ph
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On Uniqueness of the Jump Process in Quantum Measurement Theory: We prove that, contrary to the standard quantum theory of continuous
observation, in the formalism of Event Enhanced Quantum Theory the stochastic
process generating individual sample histories of pairs (observed quantum
system, observing classical apparatus) is unique. This result gives a rigorous
basis to the previous heuristic argument of Blanchard and Jadczyk. Possible
implications of this result are discussed.
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quant-ph
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Lifetime Reduction of Single Germanium-Vacancy Defects in Diamond via a
Tunable Open Microcavity: Coupling between a single quantum emitter and an optical cavity presents a
key capability for future quantum networking applications. Here, we explore
interactions between individual germanium-vacancy (GeV) defects in diamond and
an open microcavity at cryogenic temperatures. Exploiting the tunability of our
microcavity system to characterize and select emitters, we observe a
Purcell-effect-induced lifetime reduction of up to $4.5\pm0.3$, and extract
coherent coupling rates up to $350\pm20$ MHz. Our results indicate that the GeV
defect has favorable optical properties for cavity coupling, with a quantum
efficiency of at least $0.32\pm0.05$ and likely much higher.
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quant-ph
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Optimal quantum control via genetic algorithms for quantum state
engineering in driven-resonator mediated networks: We employ a machine learning-enabled approach to quantum state engineering
based on evolutionary algorithms. In particular, we focus on superconducting
platforms and consider a network of qubits -- encoded in the states of
artificial atoms with no direct coupling -- interacting via a common
single-mode driven microwave resonator. The qubit-resonator couplings are
assumed to be in the resonant regime and tunable in time. A genetic algorithm
is used in order to find the functional time-dependence of the couplings that
optimise the fidelity between the evolved state and a variety of targets,
including three-qubit GHZ and Dicke states and four-qubit graph states. We
observe high quantum fidelities (above 0.96 in the worst case setting of a
system of effective dimension 96) and resilience to noise, despite the
algorithm being trained in the ideal noise-free setting. These results show
that the genetic algorithms represent an effective approach to control quantum
systems of large dimensions.
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quant-ph
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Macroscopic quantum electrodynamics and duality in non-local and
Onsager-violating media: We formulate macroscopic quantum electrodynamics for the most general linear,
absorbing media. In particular, Onsager reciprocity is not assumed to hold. For
media with a non-local response, the field quantisation is based on the
conductivity tensor and the Green tensor for the electromagnetic field. For a
local medium response, we introduce the permittivity, permeability and
magnetoelectric susceptibilities to obtain an explicitly duality-invariant
scheme. We find that duality invariance only holds as a continuous symmetry
when non-reciprocal responses are allowed for.
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quant-ph
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On the stability of quantum holonomic gates: We provide a unified geometrical description for analyzing the stability of
holonomic quantum gates in the presence of imprecise driving controls
(parametric noise). We consider the situation in which these fluctuations do
not affect the adiabatic evolution but can reduce the logical gate performance.
Using the intrinsic geometric properties of the holonomic gates, we show under
which conditions on noise's correlation time and strength, the fluctuations in
the driving field cancel out. In this way, we provide theoretical support to
previous numerical simulations. We also briefly comment on the error due to the
mismatch between real and nominal time of the period of the driving fields and
show that it can be reduced by suitably increasing the adiabatic time.
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quant-ph
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Teaching renormalization, scaling, and universality with an example from
quantum mechanics: We discuss the quantum mechanics of a particle restricted to the half-line $x
> 0$ with potential energy $V = \alpha/x^2$ for $-1/4 < \alpha < 0$. It is
known that two scale-invariant theories may be defined. By regularizing the
near-origin behavior of the potential by a finite square well with variable
width $b$ and depth $g$, it is shown how these two scale-invariant theories
occupy fixed points in the resulting $(b,g)$-space of Hamiltonians. A
renormalization group flow exists in this space and scaling variables are shown
to exist in a neighborhood of the fixed points. Consequently, the propagator of
the regulated theory enjoys homogeneous scaling laws close to the fixed points.
Using renormalization group arguments it is possible to discern the functional
form of the propagator for long distances and long imaginary times, thus
demonstrating the extent to which fixed points control the behavior of the
cut-off theory.
By keeping the width fixed and varying only the well depth, we show how the
mean position of a bound state diverges as $g$ approaches a critical value. It
is proven that the exponent characterizing the divergence is universal in the
sense that its value is independent of the choice of regulator.
Two classical interpretations of the results are discussed: standard Brownian
motion on the real line, and the free energy of a certain one-dimensional chain
of particles with prescribed boundary conditions. In the former example, $V$
appears as part of an expectation value in the Feynman-Kac formula. In the
latter example, $V$ appears as the background potential for the chain, and the
loss of extensivity is dictated by a universal power law.
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quant-ph
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Escape from the Quantum Pigeon Conundrum: It has recently been argued in Aharonov et. al. (2016) that quantum mechanics
violates the Pigeon Counting Principle (PCP) which states that if one
distributes three pigeons among two boxes there must be at least two pigeons in
one of the boxes. However, this conclusion cannot justified by rigorous
theoretical arguments. The issue is further complicated by experimental
confirmation of the transition amplitudes predicted in this paper that
nevertheless do not support the conclusion of PCP violation. Here we prove via
a set of operator identities that the PCP is not violated within quantum
mechanics, regardless of interpretation.
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quant-ph
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Testing Continuous Spontaneous Localization with Fermi liquids: Collapse models describe phenomenologically the quantum-to-classical
transition by adding suitable nonlinear and stochastic terms to the
Schroedinger equation, thus (slightly) modifying the dynamics of quantum
systems. Experimental bounds on the collapse parameters have been derived from
various experiments involving a plethora of different systems, from single
atoms to gravitational wave detectors. Here, we give a comprehensive treatment
of the Continuous Spontaneous Localization (CSL) model, the most studied among
collapse models, for Fermi liquids. We consider both the white and non-white
noise case. Application to various astrophysical sources is presented.
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quant-ph
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Quantum Electromagnetic Fluctuations in Inhomogeneous Dielectric Media: A new mathematical and computational technique for calculating quantum vacuum
expectation values of energy and momentum densities associated with
electromagnetic fields in bounded domains containing inhomogeneous media is
discussed. This technique is illustrated by calculating the mode contributions
to the difference in the vacuum force expectation between opposite ends of an
inhomogeneous dielectric non-dispersive medium confined to a perfectly
conducting rigid box.
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quant-ph
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Analytical eigenstates for the quantum Rabi model: We develop a method to find analytical solutions for the eigenstates of the
quantum Rabi model. These include symmetric, anti-symmetric and asymmetric
analytic solutions given in terms of the confluent Heun functions. Both regular
and exceptional solutions are given in a unified form. In addition, the
analytic conditions for determining the energy spectrum are obtained. Our
results show that conditions proposed by Braak [Phys. Rev. Lett. \textbf{107},
100401 (2011)] are a type of sufficiency condition for determining the regular
solutions. The well-known Judd isolated exact solutions appear naturally as
truncations of the confluent Heun functions.
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quant-ph
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Observation of the Quantum Zeno and Anti-Zeno effects in an unstable
system: We report the first observation of the Quantum Zeno and Anti-Zeno effects in
an unstable system. Cold sodium atoms are trapped in a far-detuned standing
wave of light that is accelerated for a controlled duration. For a large
acceleration the atoms can escape the trapping potential via tunneling.
Initially the number of trapped atoms shows strong non-exponential decay
features, evolving into the characteristic exponential decay behavior. We
repeatedly measure the number of atoms remaining trapped during the initial
period of non-exponential decay. Depending on the frequency of measurements we
observe a decay that is suppressed or enhanced as compared to the unperturbed
system.
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quant-ph
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High-fidelity laser-free universal control of two trapped ion qubits: Universal control of multiple qubits -- the ability to entangle qubits and to
perform arbitrary individual qubit operations -- is a fundamental resource for
quantum computation, simulation, and networking. Here, we implement a new
laser-free scheme for universal control of trapped ion qubits based on
microwave magnetic fields and radiofrequency magnetic field gradients. We
demonstrate high-fidelity entanglement and individual control by creating
symmetric and antisymmetric two-qubit maximally entangled states with
fidelities in the intervals [0.9983, 1] and [0.9964, 0.9988], respectively, at
68% confidence, corrected for state initialization error. This technique is
robust against multiple sources of decoherence, usable with essentially any
trapped ion species, and has the potential to perform simultaneous entangling
operations on many pairs of ions without increasing control signal power or
complexity.
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quant-ph
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Comment on an alleged refutation of non-locality: A recent claim (Deutsch and Hayden (2000)), that non-locality can be refuted
by considering the evolution of the system in the Heisenberg picture, is
denied. What they demonstrated was not the falsity of non-locality but the
no-superluminal-signalling principle.
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quant-ph
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Witnessing nonclassical multipartite states: We investigate a witness for nonclassical multipartite states based on their
disturbance under local measurements. The witness operator provides a
sufficient condition for nonclassicality that coincides with a nonvanishing
global quantum discord, but it does not demand an extremization procedure.
Moreover, for the case of Z_2-symmetric systems, we rewrite the witness in
terms of correlation functions so that classicality is found to necessarily
require either vanishing magnetization in the invariant axis or isotropy of the
two-point function in the transverse spin plane. We illustrate our results in
quantum spin chains, where a characterization of factorized ground states (with
spontaneously broken Z_2 symmetry) is achieved. As a by-product, the witness
will also be shown to indicate a second-order quantum phase transitions, which
will be illustrated both for the XY and Ashkin-Teller spin chains.
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quant-ph
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Stabilizing entanglement in two-mode Gaussian states: We analyze the stabilizability of entangled two-mode Gaussian states in three
benchmark dissipative models: local damping, dissipators engineered to preserve
two-mode squeezed states, and cascaded oscillators. In the first two models, we
determine principal upper bounds on the stabilizable entanglement, while in the
last model, arbitrary amounts of entanglement can be stabilized. All three
models exhibit a tradeoff between state entanglement and purity in the
entanglement maximizing limit. Our results are derived from the
Hamiltonian-independent stabilizability conditions for Gaussian systems. Here,
we sharpen these conditions with respect to their applicability.
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quant-ph
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Quantum Cryptography with Coherent States: The safety of a quantum key distribution system relies on the fact that any
eavesdropping attempt on the quantum channel creates errors in the
transmission. For a given error rate, the amount of information that may have
leaked to the eavesdropper depends on both the particular system and the
eavesdropping strategy. In this work, we discuss quantum cryptographic
protocols based on the transmission of weak coherent states and present a new
system, based on a symbiosis of two existing ones, and for which the
information available to the eavesdropper is significantly reduced. This system
is therefore safer than the two previous ones. We also suggest a possible
experimental implementation.
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quant-ph
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A quantum cloning bound and application to quantum key distribution: We introduce a quantum cloning bound which we apply to a straightforward and
relatively direct security proof of the prepare-and-measure Bennett-Brassard
1984 (BB84) quantum key distribution (QKD) protocol against collective attacks.
The approach we propose is able to handle the practical problem of source and
detector alignment imprecisions in a simple way. Specifically, we derive a
keyrate bound for a BB84 implementation in which Alice's source emits four
given but arbitrary pure states, where the usual equivalence between
prepare-and-measure and entanglement-based QKD no longer applies. Our result is
similar to a keyrate derived by Mar{\o}y et. al. [Phys. Rev. A 82, 032337
(2010)] and generally an improvement over the keyrate derivable from the
entropic uncertainty relation in situations where it applies. We also provide a
stronger result for a source emitting arbitrary qubit states, and a further
improved result if the detector is additionally assumed two dimensional.
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quant-ph
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Reply to Norsen's paper "Are there really two different Bell's
theorems?": Yes. That is my polemical reply to the titular question in Travis Norsen's
self-styled "polemical response to Howard Wiseman's recent paper." Less
polemically, I am pleased to see that on two of my positions --- that Bell's
1964 theorem is different from Bell's 1976 theorem, and that the former does
not include Bell's one-paragraph heuristic presentation of the EPR argument ---
Norsen has made significant concessions. In his response, Norsen admits that
"Bell's recapitulation of the EPR argument in [the relevant] paragraph leaves
something to be desired," that it "disappoints" and is "problematic". Moreover,
Norsen makes other statements that imply, on the face of it, that he should
have no objections to the title of my recent paper ("The Two Bell's Theorems of
John Bell"). My principle aim in writing that paper was to try to bridge the
gap between two interpretational camps, whom I call 'operationalists' and
'realists', by pointing out that they use the phrase "Bell's theorem" to mean
different things: his 1964 theorem (assuming locality and determinism) and his
1976 theorem (assuming local causality), respectively. Thus, it is heartening
that at least one person from one side has taken one step on my bridge. That
said, there are several issues of contention with Norsen, which we (the two
authors) address after discussing the extent of our agreement with Norsen. The
most significant issues are: the indefiniteness of the word 'locality' prior to
1964; and the assumptions Einstein made in the paper quoted by Bell in 1964 and
their relation to Bell's theorem.
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quant-ph
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Testing Bell's inequality in constantly coupled Josephson circuits by
effective single-qubit operations: In superconducting circuits with interbit untunable (e.g., capacitive)
couplings, ideal local quantum operations cannot be exactly performed on
individual Josephson qubits. Here we propose an effective dynamical decoupling
approach to overcome the "fixed-interaction" difficulty for effectively
implementing elemental logical gates for quantum computation. The proposed
single-qubit operations and local measurements should allow testing Bell's
inequality with a pair of capacitively-coupled Josephson qubits. This provides
a powerful approach, besides spectral-analysis [Nature \textbf{421}, 823
(2003); Science \textbf{300}, 1548 (2003)], to verify the existence of
macroscopic quantum entanglement between two fixed-coupling Josephson qubits.
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quant-ph
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Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field
on a Torus: A classical particle in a constant magnetic field undergoes cyclotron motion
on a circular orbit. At the quantum level, the fact that all classical orbits
are closed gives rise to degeneracies in the spectrum. It is well-known that
the spectrum of a charged particle in a constant magnetic field consists of
infinitely degenerate Landau levels. Just as for the $1/r$ and $r^2$
potentials, one thus expects some hidden accidental symmetry, in this case with
infinite-dimensional representations. Indeed, the position of the center of the
cyclotron circle plays the role of a Runge-Lenz vector. After identifying the
corresponding accidental symmetry algebra, we re-analyze the system in a finite
periodic volume. Interestingly, similar to the quantum mechanical breaking of
CP invariance due to the $\theta$-vacuum angle in non-Abelian gauge theories,
quantum effects due to two self-adjoint extension parameters $\theta_x$ and
$\theta_y$ explicitly break the continuous translation invariance of the
classical theory. This reduces the symmetry to a discrete magnetic translation
group and leads to finite degeneracy. Similar to a particle moving on a cone, a
particle in a constant magnetic field shows a very peculiar realization of
accidental symmetry in quantum mechanics.
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quant-ph
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On the energy of physical states in QED in the convariant gauge: In quantum field theory it is generally assumed that there is a lower bound
to the energy of a quantum state. Here, it will be shown that there is no lower
bound to the energy of physical states in QED in a manifestly covariant gauge.
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quant-ph
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Unitary equivalence classes of split-step quantum walks: This study investigates the unitary equivalence of split-step quantum walks
(SSQW). We consider a new class of quantum walks which includes all SSQWs. We
show the explicit form of quantum walks in this class, and clarify their
unitary equivalence classes. Unitary equivalence classes of Suzuki's SSQW are
also given.
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quant-ph
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N-particle N-level singlet states: Some properties and applications: Three apparently unrelated problems which have no solution using classical
tools are described: the "N-strangers," "secret sharing," and "liar detection"
problems. A solution for each of them is proposed. Common to all three
solutions is the use of quantum states of total spin zero of N spin-(N-1)/2
particles.
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quant-ph
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Electrical Manipulation of Telecom Color Centers in Silicon: Silicon color centers have recently emerged as promising candidates for
commercial quantum technology, yet their interaction with electric fields has
yet to be investigated. In this paper, we demonstrate electrical manipulation
of telecom silicon color centers by fabricating lateral electrical diodes with
an integrated G center ensemble in a commercial silicon on insulator wafer. The
ensemble optical response is characterized under application of a
reverse-biased DC electric field, observing both 100% modulation of
fluorescence signal, and wavelength redshift of approximately 1.4 GHz/V above a
threshold voltage. Finally, we use G center fluorescence to directly image the
electric field distribution within the devices, obtaining insight into the
spatial and voltage-dependent variation of the junction depletion region and
the associated mediating effects on the ensemble. Strong correlation between
emitter-field coupling and generated photocurrent is observed. Our
demonstration enables electrical control and stabilization of semiconductor
quantum emitters.
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quant-ph
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Quantum correlations from local amplitudes and the resolution of the
Einstein-Podolsky-Rosen nonlocality puzzle: The Einstein-Podolsky-Rosen nonlocality puzzle has been recognized as one of
the most important unresolved issues in the foundational aspects of quantum
mechanics. We show that the problem is resolved if the quantum correlations are
calculated directly from local quantities which preserve the phase information
in the quantum system. We assume strict locality for the probability amplitudes
instead of local realism for the outcomes, and calculate an amplitude
correlation function.Then the experimentally observed correlation of outcomes
is calculated from the square of the amplitude correlation function. Locality
of amplitudes implies that the measurement on one particle does not collapse
the companion particle to a definite state. Apart from resolving the EPR
puzzle, this approach shows that the physical interpretation of apparently
`nonlocal' effects like quantum teleportation and entanglement swapping are
different from what is usually assumed. Bell type measurements do not change
distant states. Yet the correlations are correctly reproduced, when measured,
if complex probability amplitudes are treated as the basic local quantities. As
examples we discuss the quantum correlations of two-particle maximally
entangled states and the three-particle GHZ entangled state.
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quant-ph
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Can PT-Symmetric Quantum Mechanics be a Viable Alternative Quantum
Theory?: Update: A time-independent $n\times n$ PT-symmetric (and symmetric)
Hamiltonian is diagonalizable since it has all distinct real eigenvalues and
the resulting diagonal matrix is a real symmetric matrix. The diagonalization
results an isometry so there shouldn't be any issue with unitarity and
unfortunately this very elementary mathematical fact somehow did not draw the
authors' attention. However, PT-symmetric quantum mechanics is not out of
trouble. For time-dependent PT-symmetric (and symmetric) Hamiltonians (even
$2\times 2$ ones) the authors observed that there is a violation of unitarity.
Moreover, the first named author showed in his recent article arXiv:1312.7738
that PT-symmetric quantum mechanics is indeed a certain kind of Hermitian
quantum mechanics and that in order for time-evolution to be unitary with
respect to $J$-inner product (one that gives rise to a Hilbert space structure
on the space of state functions), the potential energy operator $V(x)$ must be
real. This means that those complex PT-symmetric Hamiltonians that have been
studied by physicists are unfortunately unphysical. The first named author
discussed in a subsequent article arXiv:1401.5149 that while finite-state
PT-symmetric quantum mechanics with time-independent Hamiltonians is not
physically any different from Hermitian quantum mechanics, PT-symmetric quantum
mechanics exhibits a distinctive symmetry from that of Hermitian quantum
mechanics.
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quant-ph
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Quantum-Limited Mirror-Motion Estimation: We experimentally demonstrate optomechanical motion and force measurements
near the quantum precision limits set by the quantum Cram\'er-Rao bounds
(QCRBs). Optical beams in coherent and phase-squeezed states are used to
measure the motion of a mirror under an external stochastic force. Utilizing
optical phase tracking and quantum smoothing techniques, we achieve position,
momentum, and force estimation accuracies close to the QCRBs with the coherent
state, while estimation using squeezed states shows clear quantum enhancements
beyond the coherent-state bounds.
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quant-ph
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On the possibility of a considerable quality improvement of a quantum
ghost image by sensing in the object arm: We consider a modification of the classical ghost imaging scheme where an
image of the research object is formed and acquired in the object arm. It is
used alongside the ghost image to produce an estimate of the transmittance
distribution of the object. It is shown that it allows to weaken the
deterioration of image quality caused by nonunit quantum efficiency of the
sensors, including the case when the quantum image obtained in the object arm
is additionally affected by the noise caused by photons that have not
interacted with the object.
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quant-ph
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Generating entangled Schrodinger cat states using a number state and a
beam splitter: Passing a photon number state through a balanced beam splitter will produce
an entangled state in which the phases of the two output beams are highly
correlated. This entangled state can be viewed as a generalized form of a
Schrodinger cat state where there is an equal probability amplitude for all
possible phases. We show that Bell's inequality can be violated using this
entangled state and two distant measuring devices that consist of a
single-photon interferometer with a Kerr medium in one path, a set of
single-photon detectors, and postselection based on a homodyne measurement.
These entangled states are sensitive to photon loss and a violation of Bell's
inequality requires either that the losses are inherently small or that their
effects have been minimized using linear optics techniques [M. Micuda et al.,
Phys. Rev. Lett. 109, 180503 (2012)]. Somewhat surprisingly, the use of the
fair sampling assumption is not required for a violation of Bell's inequality
despite the use of postselection if the measurements are made in the correct
order.
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quant-ph
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Information Theoretical Limits for Quantum Optimal Control Solutions:
Error Scaling of Noisy Channels: Accurate manipulations of an open quantum system require a deep knowledge of
its controllability properties and the information content of the implemented
control fields. By using tools of information and quantum optimal control
theory, we provide analytical bounds (information-time bounds) to characterize
our capability to control the system when subject to arbitrary sources of
noise. Moreover, since the presence of an external noise field induces open
quantum system dynamics, we also show that the results provided by the
information-time bounds are in very good agreement with the Kofman-Kurizki
universal formula describing decoherence processes. Finally, we numerically
test the scaling of the control accuracy as a function of the noise parameters,
by means of the dressed chopped random basis (dCRAB) algorithm for quantum
optimal control.
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quant-ph
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Procedure for improving cross-resonance noise resistance using
pulse-level control: Current implementations of superconducting qubits are often limited by the
low fidelities of multi-qubit gates. We present a reproducible and
runtime-efficient pulse-level approach for calibrating an improved
cross-resonance gate CR($\theta$) for arbitrary $\theta$. This CR($\theta$)
gate can be used to produce a wide range of other two-qubit gates via the
application of standard single-qubit gates. By performing an interleaved
randomised benchmarking experiment, we demonstrate that our approach leads to a
significantly higher noise resistance than the circuit-level approach currently
used by IBM. Hence, our procedure provides a genuine improvement for
applications where noise remains a limiting factor.
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quant-ph
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Phase Retrieval in Incoherent Diffractive Imaging using higher-order
photon correlation functions: To obtain spatial information about an arbitrary object in x-ray structure
analysis, the standard method is to measure the intensity in the far field,
i.e., the first-order photon correlation function of the coherently scattered
x-ray photons (coherent diffractive imaging). Recently, it was suggested to
record alternatively the incoherently scattered photons and measure the
second-order photon correlation function to reconstruct the geometry of the
unknown object (incoherent diffractive imaging). Yet, besides various
advantages of the latter method, both techniques suffer from the so-called
phase retrieval problem. Lately, an ab-initio phase retrieval algorithm to
reconstruct the phase of the so-called structure factor of the scattering
objects based on the third-order photon correlation function was reported. The
algorithm makes use of the so-called closure phase, which contains important,
yet incomplete phase information, well-known from triple correlations and their
bispectrum in speckle masking and astronomy applications. Here, we provide a
detailed analysis of the underlying scheme and quantities in the context of
x-ray structure analysis. In particular, we explicitly calculate the
third-order photon correlation function in a full quantum mechanical treatment
and discuss the uniqueness of the closure phase equations constructed from it.
In this context, we recapitulate the sign problem of the closure phase and how
it can be lifted using redundant information. We further show how the algorithm
can be improved using even higher-order photon correlation functions, e.g., the
fourth-order correlation function, delivering new phase relations appearing in
the four-point correlations.
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quant-ph
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Investigation of defect cavities formed in three-dimensional woodpile
photonic crystals: We report the optimisation of optical properties of single defects in
three-dimensional (3D) face-centred-cubic (FCC) woodpile photonic crystal (PC)
cavities by using plane-wave expansion (PWE) and finite-difference time-domain
(FDTD) methods. By optimising the dimensions of a 3D woodpile PC, wide photonic
band gaps (PBG) are created. Optical cavities with resonances in the bandgap
arise when point defects are introduced in the crystal. Three types of single
defects are investigated in high refractive index contrast (Gallium
Phosphide-Air) woodpile structures and Q-factors and mode volumes ($V_{eff}$)
of the resonant cavity modes are calculated. We show that, by introducing an
air buffer around a single defect, smaller mode volumes can be obtained. We
demonstrate high Q-factors up to 700000 and cavity volumes down to
$V_{eff}<0.2(\lambda/n)^3$. The estimates of $Q$ and $V_{eff}$ are then used to
quantify the enhancement of spontaneous emission and the possibility of
achieving strong coupling with nitrogen-vacancy (NV) colour centres in diamond.
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quant-ph
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Field test of quantum key distribution in the Tokyo QKD Network: A novel secure communication network with quantum key distribution in a
metropolitan area is reported. Different QKD schemes are integrated to
demonstrate secure TV conferencing over a distance of 45km, stable long-term
operation, and application to secure mobile phones.
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quant-ph
|
Engineering spin squeezing in a 3D optical lattice with interacting
spin-orbit-coupled fermions: One of the most important tasks in modern quantum science is to coherently
control and entangle many-body systems, and to subsequently use these systems
to realize powerful quantum technologies such as quantum-enhanced sensors.
However, many-body entangled states are difficult to prepare and preserve since
internal dynamics and external noise rapidly degrade any useful entanglement.
Here, we introduce a protocol that counterintuitively exploits inhomogeneities,
a typical source of dephasing in a many-body system, in combination with
interactions to generate metrologically useful and robust many-body entangled
states. Motivated by current limitations in state-of-the-art three-dimensional
(3D) optical lattice clocks (OLCs) operating at quantum degeneracy, we use
local interactions in a Hubbard model with spin-orbit coupling to achieve a
spin-locking effect. In addition to prolonging inter-particle spin coherence,
spin-locking transforms the dephasing effect of spin-orbit coupling into a
collective spin-squeezing process that can be further enhanced by applying a
modulated drive. Our protocol is fully compatible with state-of-the-art 3D OLC
interrogation schemes and may be used to improve their sensitivity, which is
currently limited by the intrinsic quantum noise of independent atoms. We
demonstrate that even with realistic experimental imperfections, our protocol
may generate $\sim10$--$14$ dB of spin squeezing in $\sim1$ second with
$\sim10^2$--$10^4$ atoms. This capability allows OLCs to enter a new era of
quantum enhanced sensing using correlated quantum states of driven
non-equilibrium systems.
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quant-ph
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Single phase and correlated phase estimation with multi-photon
annihilated squeezed vacuum states: An energy balancing scenario: In the last years, several works have demonstrated the advantage of photon
subtracted Gaussian states for various quantum optics and information
protocols. In most of these works, it was not clearly investigated the relation
between the advantages and the usual increasing energy of the quantum state
related to photon subtraction. In this paper, we study the performance of an
interferometer injected with multi photon annihilated squeezed vacuum states
mixed with coherent states for both single and correlated phase estimation. For
single phase estimation, albeit the use of multi-photon annihilated squeezed
vacuum states at low mean photons per mode provide advantage compared to
classical strategy, when the total input energies is held fixed, the advantage
due to photon subtraction is completely lost. However, for the correlated case
in analogous scenario, some advantage appears to come from both the energy rise
and improvement in photon statistics. In particular quantum enhanced
sensitivity with photon subtracted states appears more robust to losses,
showing an advantage of about 30% with respect to squeezed vacuum state in case
of realistic value of the detection efficiency.
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quant-ph
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Continuous-Variable Nonclassicality Detection under Coarse-Grained
Measurement: Coarse graining is a common imperfection of realistic quantum measurement,
obstructing the direct observation of quantum features. Under highly
coarse-grained measurement, we experimentally detect the continuous-variable
nonclassicality of both Gaussian and non-Gaussian states. Remarkably, we find
that this coarse-grained measurement outperforms the conventional fine-grained
measurement for nonclassicality detection: it detects nonclassicality beyond
the reach of the variance criterion, and furthermore, it exhibits stronger
statistical significance than the high-order moments method. Our work shows the
usefulness of coarse-grained measurement by providing a reliable and efficient
way of nonclassicality detection for quantum technologies.
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quant-ph
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Generalized probability rules from a timeless formulation of Wigner's
friend scenarios: The quantum measurement problem can be regarded as the tension between the
two alternative dynamics prescribed by quantum mechanics: the unitary evolution
of the wave function and the state-update rule (or "collapse") at the instant a
measurement takes place. The notorious Wigner's friend gedankenexperiment
constitutes the paradoxical scenario in which different observers (one of whom
is observed by the other) describe one and the same interaction differently,
one --the Friend-- via state-update and the other --Wigner-- unitarily. This
can lead to Wigner and his friend assigning different probabilities to the
outcome of the same subsequent measurement. In this paper, we apply the
Page-Wootters mechanism (PWM) as a timeless description of Wigner's friend-like
scenarios. We show that the standard rules to assign two-time conditional
probabilities within the PWM need to be modified to deal with the Wigner's
friend gedankenexperiment. We identify three main definitions of such modified
rules to assign two-time conditional probabilities, all of which reduce to
standard quantum theory for non-Wigner's friend scenarios. However, when
applied to the Wigner's friend setup each rule assigns different conditional
probabilities, potentially resolving the probability-assignment paradox in a
different manner. Moreover, one rule imposes strict limits on when a joint
probability distribution for the measurement outcomes of Wigner and his Friend
is well-defined, which single out those cases where Wigner's measurement does
not disturb the Friend's memory and such a probability has an operational
meaning in terms of collectible statistics. Interestingly, the same limits
guarantee that said measurement outcomes fulfill the consistency condition of
the consistent histories framework.
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quant-ph
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On some EPR (Einstein, Podolsky, Rosen) issues: A critical reconsideration of the EPR (Einstein-Podolsky-Rosen) paper shows
that the EPR argument can be developed without using the concept of `element of
physical reality', thus eliminating any philosophical element in the logical
chains of the paper. Deprived of its philosophical ornament, the EPR argument
plainly reduces to require what quantum mechanics can not do: to assign
definite values to two incompatible physical quantities. Hidden variables
theories built up according to Bell - type theorems are formulated on the basis
of the assumption that the locality condition implies the statistical
independence between two measurements space - like separated. This assumption
is valid only with the additional one that statistical dependence between two
measurements requires a causal connection between them. This additional
assumption rules out the possibility that statistical dependence may due to an
intrinsic property of the physical system under study. Therefore, hidden
variables theories are built up with a restriction which leads them to be
disproved by experiment. Quantum mechanical non - locality, invoked for
describing EPR - type experiments, is strictly connected to the hypothesis (NDV
hypothesis) according to which the twin photons of entangled pairs do not have
a definite polarization before measurements. Both hypotheses are used only for
describing EPR experiments and not for making predictions. Therefore, they can
be dropped without reducing the predictive power of quantum mechanics
concerning entangled photons pairs. Furthermore, both hypotheses can be
experimentally tested by a modification of a standard experimental apparatus
designed for studying entangled photons pairs.
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quant-ph
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Uncollapsing the wavefunction by undoing quantum measurements: We review and expand on recent advances in theory and experiments concerning
the problem of wavefunction uncollapse: Given an unknown state that has been
disturbed by a generalized measurement, restore the state to its initial
configuration. We describe how this is probabilistically possible with a
subsequent measurement that involves erasing the information extracted about
the state in the first measurement. The general theory of abstract measurements
is discussed, focusing on quantum information aspects of the problem, in
addition to investigating a variety of specific physical situations and
explicit measurement strategies. Several systems are considered in detail: the
quantum double dot charge qubit measured by a quantum point contact (with and
without Hamiltonian dynamics), the superconducting phase qubit monitored by a
SQUID detector, and an arbitrary number of entangled charge qubits.
Furthermore, uncollapse strategies for the quantum dot electron spin qubit, and
the optical polarization qubit are also reviewed. For each of these systems the
physics of the continuous measurement process, the strategy required to ideally
uncollapse the wavefunction, as well as the statistical features associated
with the measurement is discussed. We also summarize the recent experimental
realization of two of these systems, the phase qubit and the polarization
qubit.
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quant-ph
|
Entanglement, Berry Phases, and Level Crossings for the Atomic
Breit-Rabi Hamiltonian: The relation between level crossings, entanglement, and Berry phases is
investigated for the Breit-Rabi Hamiltonian of hydrogen and sodium atoms,
describing a hyperfine interaction of electron and nuclear spins in a magnetic
field. It is shown that the entanglement between nuclear and electron spins is
maximum at avoided crossings. An entangled state encircling avoided crossings
acquires a marginal Berry phase of a subsystem like an instantaneous eigenstate
moving around real crossings accumulates a Berry phase. Especially, the nodal
points of a marginal Berry phase correspond to the avoided crossing points.
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quant-ph
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Quantum mechanics and elements of reality: It is widely accepted that a Born probability of 1 is sufficient for the
existence of a corresponding element of reality. Recently Vaidman has extended
this idea to the ABL probabilities of the time-symmetrized version of quantum
mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have
objected to Vaidman's time-symmetrized elements of reality without casting
doubt on the widely accepted sufficiency condition for `ordinary' elements of
reality. In this paper I show that while the proper truth condition for a
quantum counterfactual is an ABL probability of 1, neither a Born probability
of 1 nor an ABL probability of 1 is sufficient for the existence of an element
of reality. The reason this is so is that the contingent properties of
quantum-mechanical systems are extrinsic. To obtain this result, I need to
discuss objective probabilities, retroactive causality, and the objectivity or
otherwise of the psychological arrow of time. One consequence of the extrinsic
nature of quantum-mechanical properties is that quantum mechanics presupposes
property-defining actual events (or states of affairs) and therefore cannot be
called upon to account for their occurrence (existence). Neither these events
nor the correlations between them are capable of explanation, the former
because they are causal primaries, the latter because they are fundamental:
there are no underlying causal processes. Causal connections are something we
project onto the statistical correlations, and this works only to the extent
that statistical variations can be ignored. There are nevertheless important
conclusions to be drawn from the quantum-mechanical correlations, such as the
spatial nonseparability of the world.
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quant-ph
|
Cutting Feynman Loops in Ultrastrong Cavity QED: Stimulated Emission and
Reabsorption of Virtual Particles Dressing a Physical Excitation: In quantum field theory, bare particles are dressed by a cloud of virtual
particles to form physical particles. The virtual particles affect properties
such as the mass and charge of the physical particles, and it is only these
modified properties that can be measured in experiments, not the properties of
the bare particles. The influence of virtual particles is prominent in the
ultrastrong-coupling regime of cavity quantum electrodynamics (QED), which has
recently been realized in several condensed-matter systems. In some of these
systems, the effective interaction between atom-like transitions and the cavity
photons can be switched on or off by external control pulses. This offers
unprecedented possibilities for exploring quantum vacuum fluctuations and the
relation between physical and bare particles. Here we show that, by applying
external electromagnetic pulses of suitable amplitude and frequency, each
virtual photon dressing a physical excitation in cavity-QED systems can be
converted into a physical observable photon, and back again. In this way, the
hidden relationship between the bare and the physical excitations becomes
experimentally testable. The conversion between virtual and physical photons
can be clearly pictured using Feynman diagrams with cut loops.
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quant-ph
|
Multipartite continuous-variable entanglement: Necessary and sufficient observable conditions for the nonnegativity of all
partial transpositions of multi-mode quantum states are derived. The result is
a hierarchy of inequalities for minors in terms of moments of the given state.
Violations of any inequality is a sufficient condition for entanglement. Full
entanglement can be certified for a manifold of multi-mode quantum states. A
\textit{Mathematica} package is given for a systematic test of the hierarchy of
conditions.
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quant-ph
|
New nonlinear coherent states associated to inverse bosonic and
$f$-deformed ladder operators: Using the {\it nonlinear coherent states method}, a formalism for the
construction of the coherent states associated to {\it "inverse bosonic
operators"} and their dual family has been proposed. Generalizing the approach,
the "inverse of $f$-deformed ladder operators" corresponding to the nonlinear
coherent states in the context of quantum optics and the associated coherent
states have been introduced. Finally, after applying the proposal to a few
known physical systems, particular nonclassical features as sub-Poissonian
statistics and the squeezing of the quadratures of the radiation field
corresponding to the introduced states have been investigated.
|
quant-ph
|
Learning to Program Variational Quantum Circuits with Fast Weights: Quantum Machine Learning (QML) has surfaced as a pioneering framework
addressing sequential control tasks and time-series modeling. It has
demonstrated empirical quantum advantages notably within domains such as
Reinforcement Learning (RL) and time-series prediction. A significant
advancement lies in Quantum Recurrent Neural Networks (QRNNs), specifically
tailored for memory-intensive tasks encompassing partially observable
environments and non-linear time-series prediction. Nevertheless, QRNN-based
models encounter challenges, notably prolonged training duration stemming from
the necessity to compute quantum gradients using backpropagation-through-time
(BPTT). This predicament exacerbates when executing the complete model on
quantum devices, primarily due to the substantial demand for circuit evaluation
arising from the parameter-shift rule. This paper introduces the Quantum Fast
Weight Programmers (QFWP) as a solution to the temporal or sequential learning
challenge. The QFWP leverages a classical neural network (referred to as the
'slow programmer') functioning as a quantum programmer to swiftly modify the
parameters of a variational quantum circuit (termed the 'fast programmer').
Instead of completely overwriting the fast programmer at each time-step, the
slow programmer generates parameter changes or updates for the quantum circuit
parameters. This approach enables the fast programmer to incorporate past
observations or information. Notably, the proposed QFWP model achieves learning
of temporal dependencies without necessitating the use of quantum recurrent
neural networks. Numerical simulations conducted in this study showcase the
efficacy of the proposed QFWP model in both time-series prediction and RL
tasks. The model exhibits performance levels either comparable to or surpassing
those achieved by QLSTM-based models.
|
quant-ph
|
Implementation of Single-qubit and CNOT Gates by Anyonic Excitations of
Two-body Topological Color Code: The anyonic excitations of topological two-body color code model are used to
implement a set of gates. Because of two-body interactions, the model can be
simulated in optical lattices. The excitations have nontrivial mutual
statistics, and are coupled to nontrivial gauge fields. The underlying lattice
structure provides various opportunities for encoding the states of a logical
qubit in anyonic states. The interactions make the transition between different
anyonic states, so being logical operation in the computational bases of the
encoded qubit. Two-qubit gates can be performed in a topological way using the
braiding of anyons around each other.
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quant-ph
|
Detection of genuine n-qubit entanglement via the proportionality of two
vectors: In [Science 340, 1205, 7 June (2013)], via polytopes Michael Walter et al.
proposed a sufficient condition detecting the genuinely entangled pure states.
In this paper, we indicate that generally, the coefficient vector of a pure
product state of $n$ qubits cannot be decomposed into a tensor product of two
vectors, and show that a pure state of $n$ qubits is a product state if and
only if there exists a permutation of qubits such that under the permutation,
its coefficient vector arranged in ascending lexicographical order can be
decomposed into a tensor product of two vectors. The contrapositive of this
result reads that a pure state of $n$ qubits is genuinely entangled if and only
if its coefficient vector cannot be decomposed into a tensor product of two
vectors under any permutation of qubits. Further, by dividing a coefficient
vector into $2^{i}$ equal-size block vectors, we show that the coefficient
vector can be decomposed into a tensor product of two vectors if and only if
any two non-zero block vectors of the coefficient vector are proportional. In
terms of \textquotedblleft proportionality\textquotedblright , we can rephrase
that a pure state of $n$ qubits is genuinely entangled if and only if there are
two non-zero block vectors of the coefficient vector which are not proportional
under any permutation of qubits. Thus, we avoid decomposing a coefficient
vector into a tensor product of two vectors to detect the genuine entanglement.
We also present the full decomposition theorem for product states of n qubits.
|
quant-ph
|
A proposal for the experimental detection of CSL induced random walk: Continuous Spontaneous Localization (CSL) is one possible explanation for
dynamically induced collapse of the wave-function during a quantum measurement.
The collapse is mediated by a stochastic non-linear modification of the
Schrodinger equation. A consequence of the CSL mechanism is an extremely tiny
violation of energy-momentum conservation, which can, in principle, be detected
in the laboratory via the random diffusion of a particle induced by the
stochastic collapse mechanism. In a paper in 2003, Collett and Pearle
investigated the translational CSL diffusion of a sphere, and the rotational
CSL diffusion of a disc, and showed that this effect dominates over the ambient
environmental noise at low temperatures and extremely low pressures (about
ten-thousandth of a pico-Torr). In the present paper, we revisit their analysis
and argue that this stringent condition on pressure can be relaxed, and that
the CSL effect can be seen at the pressure of about a pico-Torr. A similar
analysis is provided for diffusion produced by gravity-induced decoherence,
where the effect is typically much weaker than CSL. We also discuss the CSL
induced random displacement of a quantum oscillator. Lastly, we propose
possible experimental set-ups justifying that CSL diffusion is indeed
measurable with the current technology.
|
quant-ph
|
Protecting subspaces by acting on the outside: Many quantum control tasks aim at manipulating the state of a quantum
mechanical system within a finite subspace of states. However, couplings to the
outside are often inevitable. Here we discuss strategies which keep the system
in the controlled subspace by applying strong interactions onto the outside.
This is done by drawing analogies to simple toy models and to the quantum Zeno
effect. Special attention is paid to the constructive use of dissipation in the
protection of subspaces.
|
quant-ph
|
Local and nonlocal observables in quantum optics: It is pointed out that there exists an unambiguous definition of locality
that enables one to distinguish local and nonlocal quantities. Observables of
both types coexist in quantum optics but one must be very careful when
attempting to measure them. A nonlocal observable which formally depends on the
spatial position $\bi r$ cannot be {\em locally} measured without disturbing
the measurements of this observable at all other positions.
|
quant-ph
|
Population Oscillations and Ubiquitous Coherences in multilevel quantum
systems driven by incoherent radiation: We consider incoherent excitation of multilevel quantum systems, e.g.
molecules with multiple vibronic states.
We show that (1) the geometric constraints of the matter-field coupling
operator guarantee that noise-induced coherences will be generated in all
systems with four or more energy eigenstates and (2) noise-induced coherences
can lead to population oscillations due to quantum interference via coherence
transfer between pairs of states in the ground and excited manifolds. Our
findings facilitate the experimental detection of noise-induced coherent
dynamics in complex quantum systems.
|
quant-ph
|
The Born Rule in Quantum and Classical Mechanics: Considerable effort has been devoted to deriving the Born rule (e.g. that
$|\psi(x)|^2 dx$ is the probability of finding a system, described by $\psi$,
between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule
is not solely quantum mechanical; rather, it arises naturally in the Hilbert
space formulation of {\it classical} mechanics as well. These results provide
new insights into the nature of the Born rule, and impact on its understanding
in the framework of quantum mechanics.
|
quant-ph
|
Practical Pulse Engineering: Gradient Ascent Without Matrix
Exponentiation: Since 2005 there has been a huge growth in the use of engineered control
pulses to perform desired quantum operations in systems such as NMR quantum
information processors. These approaches, which build on the original gradient
ascent pulse engineering (GRAPE) algorithm, remain computationally intensive
because of the need to calculate matrix exponentials for each time step in the
control pulse. Here we discuss how the propagators for each time step can be
approximated using the Trotter--Suzuki formula, and a further speed up achieved
by avoiding unnecessary operations. The resulting procedure can give a
substantial speed gain with negligible cost in propagator error, providing a
more practical approach to pulse engineering.
|
quant-ph
|
OpenFlow Arbitrated Programmable Network Channels for Managing Quantum
Metadata: Quantum networks must classically exchange complex metadata between devices
in order to carry out information for protocols such as teleportation,
super-dense coding, and quantum key distribution. Demonstrating the integration
of these new communication methods with existing network protocols, channels,
and data forwarding mechanisms remains an open challenge. Software-defined
networking (SDN) offers robust and flexible strategies for managing diverse
network devices and uses. We adapt the principles of SDN to the deployment of
quantum networks, which are composed from unique devices that operate according
to the laws of quantum mechanics. We show how quantum metadata can be managed
within a software-defined network using the OpenFlow protocol, and we describe
how OpenFlow management of classical optical channels is compatible with
emerging quantum communication protocols. We next give an example specification
of the metadata needed to manage and control QPHY behavior and we extend the
OpenFlow interface to accommodate this quantum metadata. We conclude by
discussing near-term experimental efforts that can realize SDN's principles for
quantum communication.
|
quant-ph
|
Dynamics of simultaneously measured non-commuting observables: In quantum mechanics, measurements cause wavefunction collapse that yields
precise outcomes, for non-commuting observables such as position and momentum
Heisenberg's uncertainty principle limits the intrinsic precision of a state.
Although theoretical work has demonstrated the possibility to perform
simultaneous non-commuting measurements and has revealed the limits on
measurement outcomes, only recently has the dynamics of the quantum state been
discussed. To realize this unexplored regime, we simultaneously apply two
continuous quantum non-demolition probes of non-commuting observables to a
superconducting qubit. We implement multiple readout channels by coupling the
qubit to multiple modes of a cavity. To control the measurement observables, we
implement a 'single quadrature' measurement by driving the qubit and applying
cavity sidebands with a relative phase that sets the observable. Here, we show
that the uncertainty principle governs the dynamics of the wavefunction by
enforcing a lower bound on the measurement-induced disturbance. Consequently,
as we transition from measuring identical to measuring non-commuting
observables, the dynamics make a smooth transition from standard wavefunction
collapse to persistent diffusion. Although the evolution of the state differs
from that of a conventional measurement, information about both observables is
extracted by keeping track of the time ordering of the measurement record,
enabling quantum state tomography without alternating measurements. Our work
creates novel capabilities for quantum control, including rapid state
purification, adaptive measurement, measurement-based state steering and
continuous quantum error correction. As physical systems often interact
continuously with their environment via non-commuting degrees of freedom, our
work offers a way to study how notions of contemporary quantum foundations
arise in such settings.
|
quant-ph
|
Quantum localization measures in phase space: Measuring the degree of localization of quantum states in phase space is
essential for the description of the dynamics and equilibration of quantum
systems, but this topic is far from being understood. There is no unique way to
measure localization, and individual measures can reflect different aspects of
the same quantum state. Here, we present a general scheme to define
localization in measure spaces, which is based on what we call R\'enyi
occupations, from which any measure of localization can be derived. We apply
this scheme to the four-dimensional unbounded phase space of the interacting
spin-boson Dicke model. In particular, we make a detailed comparison of two
localization measures based on the Husimi function in the regime where the
model is chaotic, namely one that projects the Husimi function over the finite
phase space of the spin and another that uses the Husimi function defined over
classical energy shells. We elucidate the origin of their differences, showing
that in unbounded spaces the definition of maximal delocalization requires a
bounded reference subspace, with different selections leading to contextual
answers.
|
quant-ph
|
Expressivity of parameterized quantum circuits for generative modeling
of continuous multivariate distributions: Parameterized quantum circuits have been extensively used as the basis for
machine learning models in regression, classification, and generative tasks.
For supervised learning their expressivity has been thoroughly investigated and
several universality properties have been proven. However, in the case of
quantum generative modeling, the situation is less clear, especially when the
task is to model distributions over continuous variables. In this work, we
focus on expectation value sampling-based models; models where random variables
are sampled classically, encoded with a parametrized quantum circuit, and the
expectation value of fixed observables is measured and returned as a sample. We
prove the universality of such variational quantum algorithms for the
generation of multivariate distributions. Additionally, we provide a detailed
analysis of these models, including fundamental upper bounds on the
dimensionality of the distributions these models can represent. We further
present a tight trade-off result connecting the needed number of measurements
and qubit numbers in order to have universality for a desired dimension of
output distribution within an error tolerance. Finally we also show that the
data encoding strategy relates to the so-called polynomial chaos expansion,
which is an analog of the Fourier expansion. Our results may help guide the
design of future quantum circuits in generative modeling tasks.
|
quant-ph
|
Activating optomechanical entanglement: We propose an optomechanical setup where the activation of entanglement
through the pre-availability of non-classical correlations can be demonstrated
experimentally. We analyse the conditions under which the scheme is successful
and relate them to the current experimental state of the art. The successful
activation of entanglement embodies an interesting alternative to current
settings for the revelation of fully mechanical nonclassicality.
|
quant-ph
|
Advances in entanglement-based QKD for space applications: Quantum key distribution (QKD) enables tap-proof exchange of cryptographic
keys guaranteed by the very laws of physics. One of the last remaining
roadblocks on the way towards widespread deployment of QKD is the high loss
experienced during terrestrial distribution of photons, which limits the
distance between the communicating parties. A viable solution to this problem
is to avoid the terrestrial distribution of photons via optical fibers
altogether and instead transmit them via satellite links, where the loss is
dominated by diffraction instead of absorption and scattering. First dedicated
satellite missions have demonstrated the feasibility of this approach, albeit
with relatively low secure key rates. In order for QKD to become commercially
viable, the design of future satellite missions must be focused on achieving
higher key rates at lower system costs. Current satellite missions are already
operating at almost optimal system parameters, which leaves little room for
enhancing the key rates with currently deployed technology. Instead,
fundamentally new techniques are required to drastically reduce the costs per
secret bit shared between two distant parties. Entanglement-based protocols
provide the highest level of security and offer several pathways for increasing
the key rate by exploiting the underlying quantum correlations. In this
contribution, we review the most relevant advances in entanglement-based QKD
which are implementable over free-space links and thus enable distribution of
secure keys from orbit. The development of satellite missions is notoriously
lengthy. Possible candidates for a new generation of quantum payloads should
therefore be scrutinized as early as possible in order to advance the
development of quantum technologies for space applications.
|
quant-ph
|
Consistency, Amplitudes and Probabilities in Quantum Theory: Quantum theory is formulated as the only consistent way to manipulate
probability amplitudes. The crucial ingredient is a consistency constraint: if
there are two different ways to compute an amplitude the two answers must
agree. This constraint is expressed in the form of functional equations the
solution of which leads to the usual sum and product rules for amplitudes. A
consequence is that the Schrodinger equation must be linear: non-linear
variants of quantum mechanics are inconsistent. The physical interpretation of
the theory is given in terms of a single natural rule. This rule, which does
not itself involve probabilities, is used to obtain a proof of Born's
statistical postulate. Thus, consistency leads to indeterminism.
PACS: 03.65.Bz, 03.65.Ca.
|
quant-ph
|
Non-Unitary Quantum Computation in the Ground Space of Local
Hamiltonians: A central result in the study of Quantum Hamiltonian Complexity is that the
k-Local hamiltonian problem is QMA-complete. In that problem, we must decide if
the lowest eigenvalue of a Hamiltonian is bounded below some value, or above
another, promised one of these is true. Given the ground state of the
Hamiltonian, a quantum computer can determine this question, even if the ground
state itself may not be efficiently quantum preparable. Kitaev's proof of
QMA-completeness encodes a unitary quantum circuit in QMA into the ground space
of a Hamiltonian. However, we now have quantum computing models based on
measurement instead of unitary evolution, furthermore we can use post-selected
measurement as an additional computational tool. In this work, we generalise
Kitaev's construction to allow for non-unitary evolution including
post-selection. Furthermore, we consider a type of post-selection under which
the construction is consistent, which we call tame post-selection. We consider
the computational complexity consequences of this construction and then
consider how the probability of an event upon which we are post-selecting
affects the gap between the ground state energy and the energy of the first
excited state of its corresponding Hamiltonian. We provide numerical evidence
that the two are not immediately related, by giving a family of circuits where
the probability of an event upon which we post-select is exponentially small,
but the gap in the energy levels of the Hamiltonian decreases as a polynomial.
|
quant-ph
|
Quantum state transfer via the ferromagnetic chain in a spatially
modulated field: We show that a perfect quantum state transmission can be realized through a
spin chain possessing a commensurate structure of energy spectrum, which is
matched with the corresponding parity. As an exposition of the mirror inversion
symmetry discovered by Albanese et. al (quant-ph/0405029), the parity matched
the commensurability of energy spectra help us to present the novel
pre-engineered spin systems for quantum information transmission. Based on the
these theoretical analysis, we propose a protocol of near-perfect quantum state
transfer by using a ferromagnetic Heisenberg chain with uniform coupling
constant, but an external parabolic magnetic field. The numerical results shows
that the initial Gaussian wave packet in this system with optimal field
distribution can be reshaped near-perfectly over a longer distance.
|
quant-ph
|
On time and space double-slit experiments: Time double-slit interference experiments have been achieved and presented as
complementary to spatial double-slit interference experiments, providing a
further confirmation of the wave-particle duality. Numerical solutions of the
free particle time dependent Schr\"odinger equation were presented as
explanation of the experimental results, but have been objected to on the basis
that the standard non relativistic quantum theory does not have the property of
coherence in time. In this note the theoretical and experimental results are
derived in a schematic but analytic solution of the TDSE with appropiate
initial boundary conditions. The particular boundary conditions are justified
by the experimental setups that actually result in having only a single
electron at any given time in the double-slit arrangement; and consequently
achieve the construction of double peak single electron wave packets. The
progressive complementarity of "which-path" ("which-time") information and
"space interference" ("oscillating time transient") pattern build up is also
exhibited.
|
quant-ph
|
Economical (k,m)-threshold controlled quantum teleportation: We study a (k,m)-threshold controlling scheme for controlled quantum
teleportation. A standard polynomial coding over GF(p) with prime p > m-1 needs
to distribute a d-dimensional qudit with d >= p to each controller for this
purpose. We propose a scheme using m qubits (two-dimensional qudits) for the
controllers' portion, following a discussion on the benefit of a quantum
control in comparison to a classical control of a quantum teleportation.
|
quant-ph
|
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