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Generating entanglement between microwave photons and qubits in multiple
cavities coupled by a superconducting qutrit: We discuss how to generate entangled coherent states of four
\textrm{microwave} resonators \textrm{(a.k.a. cavities)} coupled by a
superconducting qubit. We also show \textrm{that} a GHZ state of four
superconducting qubits embedded in four different resonators \textrm{can be
created with this scheme}. In principle, \textrm{the proposed method} can be
extended to create an entangled coherent state of $n$ resonators and to prepare
a Greenberger-Horne-Zeilinger (GHZ) state of $n$ qubits distributed over $n$
cavities in a quantum network. In addition, it is noted that four resonators
coupled by a coupler qubit may be used as a basic circuit block to build a
two-dimensional quantum network, which is useful for scalable quantum
information processing.
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The thermal effect on the left-handedness of the mesoscopic composite
right-Left handed transmission line: Starting from the quantum fluctuation of current in the mesoscopic composite
right-left handed transmission line (CRLH-TL) in the thermal Fock state, we
investigate the left-handedness dependent of the frequencies, intensity and
quantum fluctuations of the current field in the CRLH-TL under different
thermal environment. The results show that the intensity and quantum
fluctuations of current field in lower frequency bands affect the
left-handedness distinctly under different thermal environment. The thermal
effect on the left-handedness in the mesoscopic CRLH-TL deserves further
experimental investigation in its miniaturization application.
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quant-ph
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Hiding and masking quantum information in complex and real quantum
mechanics: Classical information can be completely hidden in the correlations of
bipartite quantum systems. However, it is impossible to hide or mask all
quantum information according to the no-hiding and no-masking theorems derived
recently. Here we show that any set of informationally complete quantum states
is neither hidable nor maskable, thereby strengthening the no-hiding and
no-masking theorems known before. Then, by virtue of Hurwitz-Radon matrices
(representations of the Clifford algebra), we show that information about real
quantum states can be completely hidden in the correlations, although the
minimum dimension of the composite Hilbert space required increases
exponentially with the dimension of the original Hilbert space. Moreover, the
set of real quantum states is a maximal maskable set within quantum theory and
has a surprising connection with maximally entangled states. These results
offer valuable insight on the potential and limit of hiding and masking quantum
information, which are of intrinsic interest to a number of active research
areas.
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quant-ph
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Quantum jumps of saturation level rigidity and anomalous oscillations of
level number variance in the semiclassical spectrum of a modified Kepler
problem: We discover quantum Hall like jumps in the saturation spectral rigidity in
the semiclassical spectrum of a modified Kepler problem as a function of the
interval center. These jumps correspond to integer decreases of the radial
winding numbers in classical periodic motion. We also discover and explain
single harmonic dominated oscillations of the level number variance with the
width of the energy interval. The level number variance becomes effectively
zero for the interval widths defined by the frequency of the shortest periodic
orbit. This signifies that there are virtually no variations from sample to
sample in the number of levels on such intervals.
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quant-ph
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New strategy for suppressing decoherence in quantum computation: Controlable strong interaction of the qubit's bath with an external system
(i.e. with the bath's environment) allows for choosing the conditions under
which the decoherence of the qubit's states can be substantially decreased (in
a certain limit: completely avoided). By "substantially decreased" we mean that
the correlations which involve the bath's states prove negligible, while the
correlations between the qubit's and the environment's states can be made
ineffective during a comparatively long time interval. So, effectively, one may
choose the conditions under which, for sufficiently long time interval, the
initial state of "qubit + bath" remains unchanged, thus removing any kind of
the errors. The method has been successfully employed in the (simplified) model
of the solid-state-nuclear quantum computer (proposed by Kane).
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Bohmian mechanics and consistent histories: The interpretations of a particular quantum gedanken experiment provided by
Bohmian mechanics and consistent histories are shown to contradict each other,
both in the absence and in the presence of a measuring device. The consistent
history result seems closer to standard quantum mechanics, and shows no
evidence of the mysterious nonlocal influences present in the Bohmian
description.
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quant-ph
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Ultimate communication capacity of quantum optical channels by solving
the Gaussian minimum-entropy conjecture: Optical channels, such as fibers or free-space links, are ubiquitous in
today's telecommunication networks. They rely on the electromagnetic field
associated with photons to carry information from one point to another in
space. As a result, a complete physical model of these channels must
necessarily take quantum effects into account in order to determine their
ultimate performances. Specifically, Gaussian photonic (or bosonic) quantum
channels have been extensively studied over the past decades given their
importance for practical purposes. In spite of this, a longstanding conjecture
on the optimality of Gaussian encodings has yet prevented finding their
communication capacity. Here, this conjecture is solved by proving that the
vacuum state achieves the minimum output entropy of a generic Gaussian bosonic
channel. This establishes the ultimate achievable bit rate under an energy
constraint, as well as the long awaited proof that the single-letter classical
capacity of these channels is additive. Beyond capacities, it also has broad
consequences in quantum information sciences.
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Second order quantum decoherence in the boson system: The second order quantum decoherence (SOQDC)is proposed as a novel
description for the loss of quantum coherence only reflected by second order
quantum correlations. By calculating the two-time correlation function, the
phenomenon of SOQDC is studied in details for a simple model, a two boson
system interacting with a reservoir composed of one or many bosons. The second
order quantum decoherence effects can be observed in the sketched cavity QED
experiment.
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quant-ph
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Sampling-based Learning Control for Quantum Systems with Uncertainties: Robust control design for quantum systems has been recognized as a key task
in the development of practical quantum technology. In this paper, we present a
systematic numerical methodology of sampling-based learning control (SLC) for
control design of quantum systems with uncertainties. The SLC method includes
two steps of "training" and "testing". In the training step, an augmented
system is constructed using artificial samples generated by sampling
uncertainty parameters according to a given distribution. A gradient flow based
learning algorithm is developed to find the control for the augmented system.
In the process of testing, a number of additional samples are tested to
evaluate the control performance where these samples are obtained through
sampling the uncertainty parameters according to a possible distribution. The
SLC method is applied to three significant examples of quantum robust control
including state preparation in a three-level quantum system, robust
entanglement generation in a two-qubit superconducting circuit and quantum
entanglement control in a two-atom system interacting with a quantized field in
a cavity. Numerical results demonstrate the effectiveness of the SLC approach
even when uncertainties are quite large, and show its potential for robust
control design of quantum systems.
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quant-ph
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Towards a fullerene-based quantum computer: Molecular structures appear to be natural candidates for a quantum
technology: individual atoms can support quantum superpositions for long
periods, and such atoms can in principle be embedded in a permanent molecular
scaffolding to form an array. This would be true nanotechnology, with
dimensions of order of a nanometre. However, the challenges of realising such a
vision are immense. One must identify a suitable elementary unit and
demonstrate its merits for qubit storage and manipulation, including input /
output. These units must then be formed into large arrays corresponding to an
functional quantum architecture, including a mechanism for gate operations.
Here we report our efforts, both experimental and theoretical, to create such a
technology based on endohedral fullerenes or 'buckyballs'. We describe our
successes with respect to these criteria, along with the obstacles we are
currently facing and the questions that remain to be addressed.
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quant-ph
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Properties of entangled photon pairs generated in one-dimensional
nonlinear photonic-band-gap structures: We have developed a rigorous quantum model of spontaneous parametric
down-conversion in a nonlinear 1D photonic-band-gap structure based upon
expansion of the field into monochromatic plane waves. The model provides a
two-photon amplitude of a created photon pair. The spectra of the signal and
idler fields, their intensity profiles in the time domain, as well as the
coincidence-count interference pattern in a Hong-Ou-Mandel interferometer are
determined both for cw and pulsed pumping regimes in terms of the two-photon
amplitude. A broad range of parameters characterizing the emitted
down-converted fields can be used. As an example, a structure composed of 49
layers of GaN/AlN is analyzed as a suitable source of photon pairs having high
efficiency.
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Quantum Supremacy Circuit Simulation on Sunway TaihuLight: With the rapid progress made by industry and academia, quantum computers with
dozens of qubits or even larger size are being realized. However, the fidelity
of existing quantum computers often sharply decreases as the circuit depth
increases. Thus, an ideal quantum circuit simulator on classical computers,
especially on high-performance computers, is needed for benchmarking and
validation. We design a large-scale simulator of universal random quantum
circuits, often called 'quantum supremacy circuits', and implement it on Sunway
TaihuLight. The simulator can be used to accomplish the following two tasks: 1)
Computing a complete output state-vector; 2) Calculating one or a few
amplitudes. We target the simulation of 49-qubit circuits. For task 1), we
successfully simulate such a circuit of depth 39, and for task 2) we reach the
55-depth level. To the best of our knowledge, both of the simulation results
reach the largest depth for 49-qubit quantum supremacy circuits.
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Best Fidelity Conditions for Three Party Quantum Teleportation: Using the entangled three qubit states classified by Acin et al. we find the
best fidelity conditions for quantum teleportation among three parties.
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Noise limits on two-photon interferometric sensing: When a photon interferes with itself while traversing a Mach-Zehnder
inteferometer, the output port where it emerges is influenced by the phase
difference between the interferometer arms. This allows for highly precise
estimation of the path length difference (delay) but is extremely sensitive to
phase noise. By contrast, a delay between the arms of the two-photon
Hong-Ou-Mandel interferometer directly affects the relative
indistinguishability of the photon pair, affecting the rate of recorded
coincidences. This likewise allows for delay estimation; notably less precise
but with the advantage of being less sensitive to perturbations of the photons'
phase. Focusing on two-photon input states, we here investigate to what degree
of noise Mach-Zehnder interferometry retains its edge over Hong-Ou-Mandel
interferometry. We also explore the competing benefits of different two-photon
inputs for a Mach-Zehnder interferometer, and under what parameter regimes each
input performs best.
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Molecular orientation entanglement and temporal Bell-type inequalities: We detail and extend the results of [Milman {\it et al.}, Phys. Rev. Lett.
{\bf 99}, 130405 (2007)] on Bell-type inequalities based on correlations
between measurements of continuous observables performed on trapped molecular
systems. We show that for some observables with a continuous spectrum which is
bounded, one is able to construct non-locality tests sharing common properties
with those for two-level systems. The specific observable studied here is
molecular spatial orientation, and it can be experimentally measured for single
molecules, as required in our protocol. We also provide some useful general
properties of the derived inequalities and study their robustness to noise.
Finally, we detail possible experimental scenarii and analyze the role played
by different experimental parameters.
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quant-ph
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Quantum dynamics of one and two bosonic atoms in a combined
tight-binding periodic and weak parabolic potential: Strongly interacting bosonic particles in a tight-binding periodic potential
superimposed by a weak parabolic trap is a paradigm for many cold atom
experiments. Here, after revisiting the single particle problem, we study
interaction-bound dimers of bosonic atoms in the combined lattice and parabolic
potential. We consider both repulsively- and attractively-bound dimers and find
pronounced differences in their behaviour. We identify conditions under which
attractive and repulsive dimers exhibit analogous dynamics. Our studies reveal
that coherent transport and periodic oscillations of appropriately prepared
one- and two-atom wavepackets can be achieved, which may facilitate information
transfer in optical lattice based quantum computation schemes.
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quant-ph
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Tailoring three-dimensional topological codes for biased noise: Tailored topological stabilizer codes in two dimensions have been shown to
exhibit high storage threshold error rates and improved subthreshold
performance under biased Pauli noise. Three-dimensional (3D) topological codes
can allow for several advantages including a transversal implementation of
non-Clifford logical gates, single-shot decoding strategies, parallelized
decoding in the case of fracton codes as well as construction of fractal
lattice codes. Motivated by this, we tailor 3D topological codes for enhanced
storage performance under biased Pauli noise. We present Clifford deformations
of various 3D topological codes, such that they exhibit a threshold error rate
of $50\%$ under infinitely biased Pauli noise. Our examples include the 3D
surface code on the cubic lattice, the 3D surface code on a checkerboard
lattice that lends itself to a subsystem code with a single-shot decoder, the
3D color code, as well as fracton models such as the X-cube model, the
Sierpinski model and the Haah code. We use the belief propagation with ordered
statistics decoder (BP-OSD) to study threshold error rates at finite bias. We
also present a rotated layout for the 3D surface code, which uses roughly half
the number of physical qubits for the same code distance under appropriate
boundary conditions. Imposing coprime periodic dimensions on this rotated
layout leads to logical operators of weight $O(n)$ at infinite bias and a
corresponding $\exp[-O(n)]$ subthreshold scaling of the logical failure rate,
where $n$ is the number of physical qubits in the code. Even though this
scaling is unstable due to the existence of logical representations with $O(1)$
low-rate Pauli errors, the number of such representations scales only
polynomially for the Clifford-deformed code, leading to an enhanced effective
distance.
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Quantum correlations of two-qubit states with one maximally mixed
marginal: We investigate the entanglement, CHSH nonlocality, fully entangled fraction
and symmetric extendibility of two-qubit states that have a single maximally
mixed marginal. Within this set of states, the steering ellipsoid formalism has
recently highlighted an interesting family of so-called 'maximally obese'
states. These are found to have extremal quantum correlation properties that
are significant in the steering ellipsoid picture and for the study of
two-qubit states in general.
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quant-ph
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Quantum Circuit Design for Training Perceptron Models: Perceptron model is a fundamental linear classifier in machine learning and
also the building block of artificial neural networks. Recently, Wiebe et al.
(arXiv:1602.04799) proposed that the training of a perceptron can be
quadratically speeded using Grover search with a quantum computer, which has
potentially important big-data applications. In this paper, we design a quantum
circuit for implementing this algorithm. The Grover oracle, the central part of
the circuit, is realized by Quantum-Fourier-Transform based arithmetics that
specifies whether an input weight vector can correctly classify all training
data samples. We also analyze the required number of qubits and universal gates
for the algorithm, as well as the success probability using uniform sampling,
showing that it has higher possibility than spherical Gaussian distribution
$N(0,1)$. The feasibility of the circuit is demonstrated by a testing example
using the IBM-Q cloud quantum computer, where 16 qubits are used to classify
four data samples.
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Entanglement of quantum circular states of light: We present a general approach to calculating the entanglement of formation
for superpositions of two-mode coherent states, placed equidistantly on a
circle in the phase space. We show that in the particular case of
rotationally-invariant circular states the Schmidt decomposition of two modes,
and therefore the value of their entanglement, are given by analytical
expressions. We analyse the dependence of the entanglement on the radius of the
circle and number of components in the superposition. We also show that the set
of rotationally-invariant circular states creates an orthonormal basis in the
state space of the harmonic oscillator, and this basis is advantageous for
representation of other circular states of light.
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quant-ph
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Fisher information matrix as a resource measure in resource theory of
asymmetry with general connected Lie group symmetry: In recent years, in quantum information theory, there has been a remarkable
development in the general theoretical framework for studying symmetry in
dynamics. This development, called resource theory of asymmetry, is expected to
have a wide range of applications, from accurate time measurements to black
hole physics. Despite its importance, the foundation of resource theory of
asymmetry still has room for expansion. An important problem is in quantifying
the amount of resource. When the symmetry prescribed U(1), i.e., with a single
conserved quantity, the quantum Fisher information is known as a resource
measure that has suitable properties and a clear physical meaning related to
quantum fluctuation of the conserved quantity. However, it is not clear what is
the resource measure with such suitable properties when a general symmetry
prevails for which there are multiple conserved quantities. The purpose of this
paper is to fill this gap. Specifically, we show that the quantum Fisher
information matrix is a resource measure whenever a connected linear Lie group
describes the symmetry. We also consider the physical meaning of this matrix
and see which properties that the quantum Fisher information has when the
symmetry is described by $U(1)$ can be inherited by the quantum Fisher
information matrix.
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quant-ph
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Quantum local asymptotic normality based on a new quantum likelihood
ratio: We develop a theory of local asymptotic normality in the quantum domain based
on a novel quantum analogue of the log-likelihood ratio. This formulation is
applicable to any quantum statistical model satisfying a mild smoothness
condition. As an application, we prove the asymptotic achievability of the
Holevo bound for the local shift parameter.
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quant-ph
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Quantum circuit optimizations for NISQ architectures: Currently available quantum computing hardware platforms have limited 2-qubit
connectivity among their addressable qubits. In order to run a generic quantum
algorithm on such a platform, one has to transform the initial logical quantum
circuit describing the algorithm into an equivalent one that obeys the
connectivity restrictions.
In this work we construct a circuit synthesis scheme that takes as input the
qubit connectivity graph and a quantum circuit over the gate set generated by
$\{\text{CNOT},R_{Z}\}$ and outputs a circuit that respects the connectivity of
the device. As a concrete application, we apply our techniques to Google's
Bristlecone 72-qubit quantum chip connectivity, IBM's Tokyo 20-qubit quantum
chip connectivity, and Rigetti's Acorn 19-qubit quantum chip connectivity. In
addition, we also compare the performance of our scheme as a function of
sparseness of randomly generated quantum circuits.
Note: Recently, the authors of arXiv:1904.00633 independently presented a
similar optimization scheme. Our work is independent of arXiv:1904.00633, being
a longer version of the seminar presented by Beatrice Nash at the Dagstuhl
Seminar 18381: Quantum Programming Languages, pg. 120, September 2018,
Dagstuhl, Germany, slide deck available online at
https://materials.dagstuhl.de/files/18/18381/18381.BeatriceNash.Slides.pdf.
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quant-ph
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Chirality, Band Structure and Localization in Waveguide Quantum
Electrodynamics: Architectures based on waveguide quantum electrodynamics have emerged as
promising candidates for quantum networks. In this paper, we analyze the
propagation of single-photons in disordered many-atom waveguides. We pay
special attention to the influence of chirality (directionality of photon
transport) on the formation of localized photonic states, considering
separately the cases of the disorder in the atomic positions and in the atomic
transition frequencies.
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quant-ph
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A Novel Algebraic Geometry Compiling Framework for Adiabatic Quantum
Computations: Adiabatic Quantum Computing (AQC) is an attractive paradigm for solving hard
integer polynomial optimization problems. Available hardware restricts the
Hamiltonians to be of a structure that allows only pairwise interactions. This
requires that the original optimization problem to be first converted -- from
its polynomial form -- to a quadratic unconstrained binary optimization (QUBO)
problem, which we frame as a problem in algebraic geometry. Additionally, the
hardware graph where such a QUBO-Hamiltonian needs to be embedded -- assigning
variables of the problem to the qubits of the physical optimizer -- is not a
complete graph, but rather one with limited connectivity. This "problem graph
to hardware graph" embedding can also be framed as a problem of computing a
Groebner basis of a certain specially constructed polynomial ideal. We develop
a systematic computational approach to prepare a given polynomial optimization
problem for AQC in three steps. The first step reduces an input polynomial
optimization problem into a QUBO through the computation of the Groebner basis
of a toric ideal generated from the monomials of the input objective function.
The second step computes feasible embeddings. The third step computes the
spectral gap of the adiabatic Hamiltonian associated to a given embedding.
These steps are applicable well beyond the integer polynomial optimization
problem. Our paper provides the first general purpose computational procedure
that can be used directly as a $translator$ to solve polynomial integer
optimization. Alternatively, it can be used as a test-bed (with small size
problems) to help design efficient heuristic quantum compilers by studying
various choices of reductions and embeddings in a systematic and comprehensive
manner. An added benefit of our framework is in designing Ising architectures
through the study of $\mathcal Y-$minor universal graphs.
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quant-ph
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Coherence and incoherence in quadrature basis: How to manage coherence as a continuous variable quantum resource is still an
open question. We face this situation from the very definition of incoherent
states in quadrature basis. We apply several measures of coherence for some
physical states of light relative to a quadrature basis. We examine the action
on the coherence of several transformations such as beam splittings and
squeezing.
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quant-ph
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Attacking quantum key distribution by light injection via ventilation
openings: Quantum cryptography promises security based on the laws of physics with
proofs of security against attackers of unlimited computational power. However,
deviations from the original assumptions allow quantum hackers to compromise
the system. We present a side channel attack that takes advantage of
ventilation holes in optical devices to inject additional photons that can leak
information about the secret key. We experimentally demonstrate light injection
on an ID~Quantique Clavis2 quantum key distribution platform and show that this
may help an attacker to learn information about the secret key. We then apply
the same technique to a prototype quantum random number generator and show that
its output is biased by injected light. This shows that light injection is a
potential security risk that should be addressed during the design of quantum
information processing devices.
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On pseudo-stochastic matrices and pseudo-positive maps: Stochastic matrices and positive maps in matrix algebras proved to be very
important tools for analysing classical and quantum systems. In particular they
represent a natural set of transformations for classical and quantum states,
respectively. Here we introduce the notion of pseudo-stochastic matrices and
consider their semigroup property. Unlike stochastic matrices,
pseudo-stochastic matrices are permitted to have matrix elements which are
negative while respecting the requirement that the sum of the elements of each
column is one. They also allow for convex combinations, and carry a Lie group
structure which permits the introduction of Lie algebra generators. The quantum
analog of a pseudo-stochastic matrix exists and is called a pseudo-positive
map. They have the property of transforming a subset of quantum states
(characterized by maximal purity or minimal von Neumann entropy requirements)
into quantum states. Examples of qubit dynamics connected with "diamond" sets
of stochastic matrices and pseudo-positive maps are dealt with.
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Quantum Mechanics: 44 Admissible Questions? -Not only Fapp-: The words: determinism, hidden variables, subjectivism, information,
objectivism, informational-theoretic axioms,observers have some connection with
physical reality? What we mean with "description" of physical reality? When we
say that we understand this reality? Certain parameters:position, velocity are
sufficient? We will focus only to conceptual considerations regarding the
relation between the "questions" and the relative "answers" in general and
specifically in quantum mechanics. It is usually believed that the answers are
more important of the questions, for this reason we can read many answers
everywhere and in different field of knowledge. We need to add and clarify some
things: (i) usually an answers require a question, (ii) but, as we know, their
relation is not so simple and immediate, (iii) For instance: a)an epistemic
questions give us ontic answers? b)the answer has a connection with the
question and vice versa? c)we could to infer a question starting from an
answer? d)there are answers without questions? These answers could be in some
framework considered as ontic answers? The relative scientific works are the
same time ontic? Speaking of quantum mechanics we see around many answers in
the meantime we do not see the correspondent questions, these answers seem
completely independent, and this seem a right road, the road of the independent
nature unlinked from human thoughts. We retain instead that questions can
affect the possible answers. Exist "something" before the question?
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quant-ph
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Basis States for Relativistic, Dynamically-Entangled Particles: In several recent papers on entanglement in relativistic quantum systems and
relativistic Bell's inequalities, relativistic Bell-type two-particle states
have been constructed in analogy to non-relativistic states. These
constructions do not have the form suggested by relativistic invariance of the
dynamics. Two relativistic formulations of Bell-type states are shown for
massive particles, one using the standard Wigner spin basis and one using the
helicity basis. The construction hinges on the use of Clebsch-Gordan
coefficients of the Poincar\'e group to reduce the direct product of two
unitary irreducible representations (UIRs) into a direct sum of UIRs.
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quant-ph
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Zero field entanglement in dipolar coupling spin system at negative
temperatures: A dipolar coupled spin system can achieve internal thermodynamic equilibrium
states at negative absolute temperature. We study analytically and numerically
the temperature dependence of the concurrence in a dipolar coupled spin-1/2
system in both non-zero and zero fields and show that, at negative
temperatures, entangled states can exist even in zero magnetic field.
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quant-ph
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Quantum error mitigation by layerwise Richardson extrapolation: A widely used method for mitigating errors in noisy quantum computers is
Richardson extrapolation, a technique in which the overall effect of noise on
the estimation of quantum expectation values is captured by a single parameter
that, after being scaled to larger values, is eventually extrapolated to the
zero-noise limit. We generalize this approach by introducing \emph{layerwise
Richardson extrapolation (LRE)}, an error mitigation protocol in which the
noise of different individual layers (or larger chunks of the circuit) is
amplified and the associated expectation values are linearly combined to
estimate the zero-noise limit. The coefficients of the linear combination are
analytically obtained from the theory of multivariate Lagrange interpolation.
LRE leverages the flexible configurational space of layerwise unitary folding,
allowing for a more nuanced mitigation of errors by treating the noise level of
each layer of the quantum circuit as an independent variable. We provide
numerical simulations demonstrating scenarios where LRE achieves superior
performance compared to traditional (single-variable) Richardson extrapolation.
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Experimental quantum state transfer of an arbitrary single-qubit state
on a cycle with four vertices using a coined quantum random walk: We experimentally demonstrate the transfer of an unknown single-qubit state
from Alice to Bob via a two-step discrete-time quantum random walk on a cycle
with four vertices on a four-qubit nuclear magnetic resonance quantum
processor. The qubits with Alice and Bob are used as coin qubits and the walk
is carried out on in a two-qubit `Gaming Arena'. In this scheme, the required
entangled state is generated naturally via conditional shift operators during
the quantum walk, instead of being prepared in advance. We implement controlled
operators at Bob's end, which are controlled by Alice's coin qubit and arena
qubits, in order to reconstruct Alice's randomly generated state at Bob's end.
To characterize the state transfer process, we perform quantum process
tomography by repeating the experiment for a set of input states $\{ \vert
0\rangle, \vert 1\rangle, \vert +\rangle, \vert -\rangle \}$. Using an
entanglement witness, we certify that the quantum walk generates a genuine
quadripartite entangled state of all four qubits. To evaluate the efficacy of
the transfer scheme, We use quantum state tomography to reconstruct the
transferred state by calculating the projection of the experimentally
reconstructed four-qubit density matrix onto three-qubit basis states. Our
results demonstrate that the quantum circuit is able to perform quantum state
transfer via the two-step quantum random walk with high fidelity.
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Quantum Algorithm for SAT Problem and Quantum Mutual Entropy: It is von Neumann who opened the window for today's Information epoch. He
defined quantum entropy including Shannon's information more than 20 years
ahead of Shannon, and he introduced a concept what computation means
mathematically. In this paper I will report two works that we have recently
done, one of which is on quantum algorithum in generalized sense solving the
SAT problem (one of NP complete problems) and another is on quantum mutual
entropy properly describing quantum communication processes.
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The Evolution of the Bell Notion of Beable: from Bohr to Primitive
Ontology: John S. Bell introduced the notion of beable, as opposed to the standard
notion of observable, in order to emphasize the need for an unambiguous
formulation of quantum mechanics. In the paper I show that Bell formulated in
fact two different theories of beables. The first is somehow reminiscent of the
Bohr views on quantum mechanics but, at the same time, is curiously adopted by
Bell as a critical tool against the Copenhagen interpretation, whereas the
second, more mature formulation was among the sources of inspiration of the
so-called Primitive Ontology (PO) approach to quantum mechanics, an approach
inspired to scientific realism. In the first part of the paper it is argued
that, contrary to the Bell wishes, the first formulation of the theory fails to
be an effective recipe for addressing the ambiguity underlying the standard
formulation of quantum mechanics, whereas it is only the second formulation
that successfully paves the way to the PO approach. In the second part, I
consider how the distinction between the two formulations of the Bell theory of
beables fares vis-a-vis the complex relationship between the theory of beables
and the details of the PO approach.
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All-optical generation of states for "Encoding a qubit in an oscillator": Both discrete and continuous systems can be used to encode quantum
information. Most quantum computation schemes propose encoding qubits in
two-level systems, such as a two-level atom or an electron spin. Others exploit
the use of an infinite-dimensional system, such as a harmonic oscillator. In
"Encoding a qubit in an oscillator" [Phys. Rev. A 64 012310 (2001)], Gottesman,
Kitaev, and Preskill (GKP) combined these approaches when they proposed a
fault-tolerant quantum computation scheme in which a qubit is encoded in the
continuous position and momentum degrees of freedom of an oscillator. One
advantage of this scheme is that it can be performed by use of relatively
simple linear optical devices, squeezing, and homodyne detection. However, we
lack a practical method to prepare the initial GKP states. Here we propose the
generation of an approximate GKP state by using superpositions of optical
coherent states (sometimes called "Schr\"odinger cat states"), squeezing,
linear optical devices, and homodyne detection.
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Complexity of measurement of a qubit pair: Analysis of the process of accumulation of the results of measurements shows
that the success of this process substantially depends on the possibility of
coordination of actions of two participants of the process - preparator who
prepares the series of the states being measured and registrator who chooses in
each event of measurement one of incompatible observables.
A new value, the complexity of measurement of a state, is used, this
characterizes the number of the measurement events needed for solution of the
reconstruction problem. By means of this value it is shown that the dependence
of the upper limit of the needed number of measurements on the permissible
error is a square law one, so a twofold decrease of permissible error
corresponds to a fourfold increase of needed number of measurements.
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quant-ph
|
Generalized uncertainty relation between thermodynamic variables in
quantum thermodynamics: Macroscopic thermodynamics, via the weak coupling approximation, assumes that
the equi?librium properties of a system are not affected by interactions with
its environment. However, this assumption may not hold for quantum systems,
where the strength of interaction between the system and the environment may
become non-negligible in a strong coupling regime. In such a regime, the
equilibrium properties of the system depend on the interaction energy and the
system state is no longer of the Gibbs form. Regarding such interactions, using
tools from the quantum estimation theory, we derive the thermodynamic
uncertainty relation between intensive and exten?sive variables valid at all
coupling regimes through the generalized Gibbs ensemble (GGE). Where we
demonstrate the lower bound on the uncertainty of intensive variables increases
in presence of quantum fluctuations. Also, we calculate the general uncertainty
relations for several ensembles to corroborate the literature results, thus
showing the versatility of our method.
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quant-ph
|
Matchgate quantum computing and non-local process analysis: In the circuit model, quantum computers rely on the availability of a
universal quantum gate set. A particularly intriguing example is a set of
two-qubit only gates: matchgates, along with SWAP (the exchange of two qubits).
In this paper, we show a simple decomposition of arbitrary matchgates into
better known elementary gates, and implement a matchgate in a linear-optics
experiment using single photons. The gate performance was fully characterized
via quantum process tomography. Moreover, we represent the resulting
reconstructed quantum process in a novel way, as a fidelity map in the space of
all possible nonlocal two-qubit unitaries. We propose the non-local distance -
which is independent of local imperfections like uncorrelated noise or
uncompensated local rotations - as a new diagnostic process measure for the
non-local properties of the implemented gate.
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quant-ph
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Deterministic Bethe state preparation: We present a quantum circuit that prepares an arbitrary $U(1)$-invariant
state on a quantum computer, including the exact eigenstates of the spin-1/2
XXZ quantum spin chain with either open or closed boundary conditions. The
algorithm is deterministic, does not require ancillary qubits, and does not
require QR decompositions. The circuit prepares such an $L$-qubit state with
$M$ down-spins using $\binom{L}{M}-1$ multi-controlled rotation gates and
$2M(L-M)$ CNOT-gates.
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quant-ph
|
Separability criterion using one observable for special states:
Entanglement detection via quantum quench: Detecting entanglement in many-body quantum systems is crucial but
challenging, typically requiring multiple measurements. Here, we establish the
class of states where measuring connected correlations in just $\textit{one}$
basis is sufficient and necessary to detect bipartite separability, provided
the appropriate basis and observables are chosen. This methodology leverages
prior information about the state, which, although insufficient to reveal the
complete state or its entanglement, enables our one basis approach to be
effective. We discuss the possibility of one observable entanglement detection
in a variety of systems, including those without conserved charges, such as the
Transverse Ising model, reaching the appropriate basis via quantum quench. This
provides a much simpler pathway of detection than previous works. It also shows
improved sensitivity from Pearson Correlation detection techniques.
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quant-ph
|
Thermodynamics analogue for self-trapped spinning-stationary Madelung
fluid: We discuss two-dimensional Madelung fluid dynamics whose irrotational case
reduces into the Schr\"odinger equation for a free single particle. We show
that the self-trapped spinning-stationary Madelung fluid reported in the
previous paper can be analogically identified as an equilibrium thermodynamics
system. This is done by making correspondence between Shannon entropy over
Madelung density and internal energy to be defined in the main text,
respectively with thermal-entropy and thermal-internal energy of equilibrium
thermodynamics system. This leads us to identify a Madelung fluid analog of
thermal-temperature at the vanishing value of which the stationary Madelung
fluid will be no more spinning and is equal to the quantum mechanical ground
state of a particle trapped inside a cylindrical tube external potential.
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quant-ph
|
Controlled and combined remote implementations of partially unknown
quantum operations of multiqubits using GHZ states: We propose and prove protocols of controlled and combined remote
implementations of partially unknown quantum operations belonging to the
restricted sets [An Min Wang: PRA, \textbf{74}, 032317(2006)] using GHZ states.
We detailedly describe the protocols in the cases of one qubit, respectively,
with one controller and with two senders. Then we extend the protocols to the
cases of multiqubits with many controllers and two senders. Because our
protocols have to demand the controller(s)'s startup and authorization or two
senders together working and cooperations, the controlled and combined remote
implementations of quantum operations definitely can enhance the security of
remote quantum information processing and potentially have more applications.
Moreover, our protocol with two senders is helpful to farthest arrive at the
power of remote implementations of quantum operations in theory since the
different senders perhaps have different operational resources and different
operational rights in practice.
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quant-ph
|
The interface of gravity and quantum mechanics illuminated by Wigner
phase space: We provide an introduction into the formulation of non-relativistic quantum
mechanics using the Wigner phase-space distribution function and apply this
concept to two physical situations at the interface of quantum theory and
general relativity: (i) the motion of an ensemble of cold atoms relevant to
tests of the weak equivalence principle, and (ii) the Kasevich-Chu
interferometer. In order to lay the foundations for this analysis we first
present a representation-free description of the Kasevich-Chu interferometer
based on unitary operators.
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quant-ph
|
A Sharp Fannes-type Inequality for the von Neumann Entropy: We derive an inequality relating the entropy difference between two quantum
states to their trace norm distance, sharpening a well-known inequality due to
M. Fannes. In our inequality, equality can be attained for every prescribed
value of the trace norm distance.
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quant-ph
|
Quantum Brownian motion in a magnetic field: Transition from monotonic
to oscillatory behaviour: We investigate the Brownian motion of a charged particle in a magnetic field.
We study this in the high temperature classical and low temperature quantum
domains. In both domains, we observe a transition of the mean square
displacement from a monotonic behaviour to a damped oscillatory behaviour as
one increases the strength of the magnetic field. When the strength of the
magnetic field is negligible, the mean square displacement grows linearly with
time in the classical domain and logarithmically with time in the quantum
domain. We notice that these features of the mean square displacement are
robust and remain essentially the same for an Ohmic dissipation model and a
single relaxation time model for the memory kernel. The predictions stemming
from our analysis can be tested against experiments in trapped cold ions.
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quant-ph
|
Maximal violation of Clauser-Horne-Shimony-Holt inequality for two
qutrits: Bell-Clauser-Horne-Shimony-Holt inequality (in terms of correlation
functions) of two qutrits is studied in detail by employing tritter
measurements. A uniform formula for the maximum value of this inequality for
tritter measurements is obtained. Based on this formula, we show that
non-maximally entangled states violate the Bell-CHSH inequality more strongly
than the maximally entangled one. This result is consistent with what was
obtained by Ac{\'{i}}n {\it et al} [Phys. Rev. A {\bf 65}, 052325 (2002)] using
the Bell-Clauser-Horne inequality (in terms of probabilities).
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quant-ph
|
Kinematic variables in noncommutative phase space and parameters of
noncommutativity: We consider a space with noncommutativity of coordinates and noncommutativity
of momenta. It is shown that coordinates in noncommutative phase space depend
on mass therefore they can not be considered as kinematic variables. Also,
noncommutative momenta are not proportional to a mass as it has to be. We find
conditions on the parameters of noncommutativity on which these problems are
solved. It is important that on the same conditions the weak equivalence
principle is not violated, the properties of kinetic energy are recovered, and
the motion of the center-of-mass of composite system and relative motion are
independent in noncommutative phase space.
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quant-ph
|
Practical long-distance quantum key distribution through concatenated
entanglement swapping with parametric down-conversion sources: We develop a theory for long-distance quantum key distribution based on
concatenated entanglement swapping using parametric down-conversion sources and
show numerical results of our model. The model incorporates practical resources
including multi-pair sources, inefficient detectors with dark counts and lossy
channels. We calculate the maximum secret key-generation ratefor up to three
entanglement swapping stations by optimizing over resource parameters, and our
numerical simulation shows that the range of quantum key distribution can in
principle be markedly increased but at the expense of an atrociously unfeasible
secret key-generation rate; however, the upper bound of our key rates closely
approach the Takeoka-Guha-Wilde upper bound. Our analysis demonstrates the need
for new technology such as quantum memory to synchronize photons and our
methods should serve as a valuable component for accurately modelling
quantum-memory-based long-distance quantum key distribution.
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quant-ph
|
Sharp implications of AGSPs for degenerate ground spaces: We generalize the `off-the-rack' AGSP$\Rightarrow$entanglement bound
implication of [Arad, Landau, and Vazirani '12] from unique ground states to
degenerate ground spaces. Our condition $R\Delta\le1/2$ on a $(\Delta,R)$-AGSP
matches the non-degenerate case, whereas existing tools in the literature of
spin chains would only be adequate to prove a less natural implication which
assumes $R^{\text{Const}}\Delta\le c$. To show that $R\Delta\le1/2$ still
suffices in the degenerate case we prove an optimal error reduction bound which
improves on the literature by a factor $\delta\mu$ where $\delta=1-\mu$ is the
viability. The generalized off-the-rack bound implies the generalization of a
recent 2D subvolume law of [Anshu, Arad, and Gosset '19] from the
non-degenerate case to the sub-exponentially degenerate case.
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quant-ph
|
Trapping and observing single atoms in the dark: A single atom strongly coupled to a cavity mode is stored by
three-dimensional confinement in blue-detuned cavity modes of different
longitudinal and transverse order. The vanishing light intensity at the trap
center reduces the light shift of all atomic energy levels. This is exploited
to detect a single atom by means of a dispersive measurement with 95%
confidence in 0.010 ms, limited by the photon-detection efficiency. As the atom
switches resonant cavity transmission into cavity reflection, the atom can be
detected while scattering about one photon.
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quant-ph
|
Minimizing readout-induced noise for early fault-tolerant quantum
computers: Quantum error correcting code can diagnose potential errors and correct them
based on measured outcomes by leveraging syndrome measurement. However,
mid-circuit measurement has been technically challenging for early
fault-tolerant quantum computers and the readout-induced noise acts as a main
contributor to the logical infidelity. We present a different method for
syndrome extraction, namely Generalized Syndrome Measurement, that requires
only a single-shot measurement on a single ancilla, while the canonical
syndrome measurement requires multiple measurements to extract the eigenvalue
for each stabilizer generator. As such, we can detect the error in the logical
state with minimized readout-induced noise. By adopting our method as a
pre-check routine for quantum error correcting cycles, we can significantly
reduce the readout overhead, the idling time, and the logical error rate during
syndrome measurement. We numerically analyze the performance of our protocol
using Iceberg code and Steane code under realistic noise parameters based on
superconducting hardware and demonstrate the advantage of our protocol in the
near-term scenario. As mid-circuit measurements are still error-prone for
near-term quantum hardware, our method may boost the applications of early
fault-tolerant quantum computing.
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quant-ph
|
Analysis of Dirac exceptional points and their isospectral Hermitian
counterparts: Recently, a Dirac exceptional point (EP) was reported in a non-Hermitian
system. Unlike a Dirac point in Hermitian systems, this Dirac EP has coalesced
eigenstates in addition to the degenerate energy. Also different from a typical
EP, the two energy levels connected at this Dirac EP remain real in its
vicinity and display a linear instead of square root dispersion, forming a
tilted Dirac cone in the hybrid space consisting of a momentum dimension and a
synthetic dimension for the strength of non-Hermiticity. In this report, we
first present simple three-band and two-band matrix models with a Dirac EP,
where the linear dispersion of the tilted Dirac cone can be expressed
analytically. Importantly, our analysis also reveals that there exist Hermitian
and non-Hermitian systems that have the same (real-valued) energy spectrum in
their entire parameter space, with the exception that one or more degeneracies
in the former are replaced by Dirac EPs in the later. Finally, we show the
existence of an imaginary Dirac cone with an EP at its center.
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quant-ph
|
Strong extinction of a laser beam by a single molecule: We present an experiment where a single molecule strongly affects the
amplitude and phase of a laser field emerging from a subwavelength aperture. We
achieve a visibility of -6% in direct and +10% in cross-polarized detection
schemes. Our analysis shows that a close to full extinction should be possible
using near-field excitation.
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quant-ph
|
Orthocomplementation and compound systems: In their 1936 founding paper on quantum logic, Birkhoff and von Neumann
postulated that the lattice describing the experimental propositions concerning
a quantum system is orthocomplemented. We prove that this postulate fails for
the lattice L_sep describing a compound system consisting of so called
separated quantum systems. By separated we mean two systems prepared in
different ``rooms'' of the lab, and before any interaction takes place. In that
case the state of the compound system is necessarily a product state. As a
consequence, Dirac's superposition principle fails, and therefore L_sep cannot
satisfy all Piron's axioms. In previous works, assuming that L_sep is
orthocomplemented, it was argued that L_sep is not orthomodular and fails to
have the covering property. Here we prove that L_sep cannot admit and
orthocomplementation. Moreover, we propose a natural model for L_sep which has
the covering property.
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quant-ph
|
Tight conic approximation of testing regions for quantum statistical
models and measurements: Quantum statistical models (i.e., families of normalized density matrices)
and quantum measurements (i.e., positive operator-valued measures) can be
regarded as linear maps: the former, mapping the space of effects to the space
of probability distributions; the latter, mapping the space of states to the
space of probability distributions. The images of such linear maps are called
the testing regions of the corresponding model or measurement. Testing regions
are notoriously impractical to treat analytically in the quantum case. Our
first result is to provide an implicit outer approximation of the testing
region of any given quantum statistical model or measurement in any finite
dimension: namely, a region in probability space that contains the desired
image, but is defined implicitly, using a formula that depends only on the
given model or measurement. The outer approximation that we construct is
minimal among all such outer approximations, and close, in the sense that it
becomes the maximal inner approximation up to a constant scaling factor.
Finally, we apply our approximation formulas to characterize, in a semi-device
independent way, the ability to transform one quantum statistical model or
measurement into another.
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quant-ph
|
Introduction to error correcting codes in quantum computers: The goal of this paper is to review the theoretical basis for achieving a
faithful quantum information transmission and processing in the presence of
noise. Initially encoding and decoding, implementing gates and quantum error
correction will be considered error free. Finally we will relax this non
realistic assumption, introducing the quantum fault-tolerant concept. The
existence of an error threshold permits to conclude that there is no physical
law preventing a quantum computer from being built. An error model based on the
depolarizing channel will be able to provide a simple estimation of the storage
or memory computation error threshold: < 5.2 10-5. The encoding is made by
means of the [[7,1,3]] Calderbank-Shor-Steane quantum code and the Shor's
fault-tolerant method to measure the stabilizer's generators is used.
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quant-ph
|
Compact Orthoalgebras: We initiate a study of topological orthoalgebras (TOAs), concentrating on the
compact case. Examples of TOAs include topological orthomodular lattices, and
also the projection lattice of a Hilbert space. As the latter example
illustrates, a lattice-ordered TOA need not be a topological lattice. However,
we show that a compact Boolean TOA is a topological Boolean algebra. Using
this, we prove that any compact regular TOA is atomistic, and has a compact
center. We prove also that any compact TOA with isolated 0 is of finite height.
We then focus on stably ordered TOAs: those in which the upper-set generated by
an open set is open. These include both topological orthomodular lattices and
interval orthoalgebras -- in particular, projection lattices. We show that the
topology of a compact stably-ordered TOA with isolated 0 is determined by that
of of its space of atoms.
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quant-ph
|
Cooperative atom-light interaction in a blockaded Rydberg ensemble: By coupling a probe transition to a Rydberg state using electro-magnetically
induced transparency (EIT) we map the strong dipole-dipole interactions onto an
optical field. We characterize the resulting cooperative optical non-linearity
as a function of probe strength and density. We show that the effect of dipole
blockade cannot be described using a mean-field but requires an $N$-atom
cooperative model. Good quantitative agreement is obtained for three atoms per
blockade with the $n=60$ Rydberg state. We place an upper-limit on the
dephasing rate of the blockade spheres of $<110$ kHz.
|
quant-ph
|
Rapid adiabatic passage without level crossing: We present a method for achieving complete population transfer in a two-state
quantum system via adiabatic time evolution in which, contrary to conventional
rapid adiabatic passage produced by chirped pulses, there occurs no crossing of
diabatic energy curves: there is no sign change of the detuning. Instead, we
use structured pulses, in which, in addition to satisfying conditions for
adiabatic evolution, there occurs a sign change of the Rabi frequency when the
detuning is zero. We present simulations that offer simple geometrical
interpretation of the two-dimensional motion of the Bloch vector for this
system, illustrating how both complete population inversion and complete
population return occur for different choices of structured pulses.
|
quant-ph
|
General Scheme for Super Dense Coding between Multi-Parties: Dense coding or super-dense coding in the case of high-dimension quantum
states between two parties and multi-parties has been studied in this paper. We
construct explicitly the measurement basis and the forms of the single-body
unitary operations corresponding to the basis chosen, and the rules for
selecting the one-body unitary operations in a multi-party case.
|
quant-ph
|
Necessary detection efficiencies for secure quantum key distribution and
bound randomness: In recent years, several hacking attacks have broken the security of quantum
cryptography implementations by exploiting the presence of losses and the
ability of the eavesdropper to tune detection efficiencies. We present a simple
attack of this form that applies to any protocol in which the key is
constructed from the results of untrusted measurements performed on particles
coming from an insecure source or channel. Because of its generality, the
attack applies to a large class of protocols, from standard prepare-and-measure
to device-independent schemes. Our attack gives bounds on the critical
detection efficiencies necessary for secure quantum distribution, which show
that the implementation of most partly device independent solutions is, from
the point of view of detection efficiency, almost as demanding as fully
device-independent ones. We also show how our attack implies the existence of a
form of bound randomness, namely non-local correlations in which a
non-signalling eavesdropper can find out a posteriori the result of any
implemented measurement.
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quant-ph
|
On the group theoretic structure of a class of quantum dialogue
protocols: Intrinsic symmetry of the existing protocols of quantum dialogue are
explored. It is shown that if we have a set of mutually orthogonal $n$-qubit
states {\normalsize
$\{|\phi_{0}>,|\phi_{1}>,....,|\phi_{i}<,...,|\phi_{2^{n}-1}>\}$ and a set of
$m-qubit$ ($m\leq n$) unitary operators
$\{U_{0},U_{2},...,U_{2^{n}-1}\}:U_{i}|\phi_{0}>=|\phi_{i}>$ and
$\{U_{0},U_{2},...,U_{2^{n}-1}\}$ forms a group under multiplication then it
would be sufficient to construct a quantum dialogue protocol using this set of
quantum states and this group of unitary operators}. The sufficiency condition
is used to provide a generalized protocol of quantum dialogue. Further the
basic concepts of group theory and quantum mechanics are used here to
systematically generate several examples of possible groups of unitary
operators that may be used for implementation of quantum dialogue. A large
number of examples of quantum states that may be used to implement the
generalized quantum dialogue protocol using these groups of unitary operators
are also obtained. For example, it is shown that GHZ state, GHZ-like state, W
state, 4 and 5 qubit Cluster states, Omega state, Brown state, $Q_{4}$ state
and $Q_{5}$ state can be used for implementation of quantum dialogue protocol.
The security and efficiency of the proposed protocol is appropriately analyzed.
It is also shown that if a group of unitary operators and a set of mutually
orthogonal states are found to be suitable for quantum dialogue then they can
be used to provide solutions of socialist millionaire problem.
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quant-ph
|
Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware: The quantum circuit model is the de-facto way of designing quantum
algorithms. Yet any level of abstraction away from the underlying hardware
incurs overhead. In the era of near-term, noisy, intermediate-scale quantum
(NISQ) hardware with severely restricted resources, this overhead may be
unjustifiable. In this work, we develop quantum algorithms for Hamiltonian
simulation "one level below" the circuit model, exploiting the underlying
control over qubit interactions available in principle in most quantum hardware
implementations. We then analyse the impact of these techniques under the
standard error model where errors occur per gate, and an error model with a
constant error rate per unit time.
To quantify the benefits of this approach, we apply it to a canonical
example: time-dynamics simulation of the 2D spin Fermi-Hubbard model. We derive
analytic circuit identities for efficiently synthesising multi-qubit evolutions
from two-qubit interactions. Combined with new error bounds for Trotter product
formulas tailored to the non-asymptotic regime and a careful analysis of error
propagation under the aforementioned per-gate and per-time error models, we
improve upon the previous best methods for Hamiltonian simulation by multiple
orders of magnitude. By our calculations, for a 5$\mathbf\times$5 Fermi-Hubbard
lattice we reduce the circuit depth from 800,160 to 1460 in the per-gate error
model, or the circuit-depth-equivalent to 440 in the per-time error model. This
brings Hamiltonian simulation, previously beyond reach of current hardware for
non-trivial examples, significantly closer to being feasible in the NISQ era.
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quant-ph
|
Restoration of the non-Hermitian bulk-boundary correspondence via
topological amplification: Non-Hermitian (NH) lattice Hamiltonians display a unique kind of energy gap
and extreme sensitivity to boundary conditions. Due to the NH skin effect, the
separation between edge and bulk states is blurred and the (conventional)
bulk-boundary correspondence is lost. Here, we restore the bulk-boundary
correspondence for the most paradigmatic class of NH Hamiltonians, namely those
with one complex band and without symmetries. We obtain the desired NH
Hamiltonian from the (mean-field) unconditional evolution of driven-dissipative
cavity arrays, in which NH terms -- in the form of non-reciprocal hopping
amplitudes, gain and loss -- are explicitly modeled via coupling to (engineered
and non-engineered) reservoirs. This approach removes the arbitrariness in the
definition of the topological invariant, as point-gapped spectra differing by a
complex-energy shift are not treated as equivalent; the origin of the complex
plane provides a common reference (base point) for the evaluation of the
topological invariant. This implies that topologically non-trivial Hamiltonians
are only a strict subset of those with a point gap and that the NH skin effect
does not have a topological origin. We analyze the NH Hamiltonians so obtained
via the singular value decomposition, which allows to express the NH
bulk-boundary correspondence in the following simple form: an integer value
$\nu$ of the topological invariant defined in the bulk corresponds to $\vert
\nu\vert$ singular vectors exponentially localized at the system edge under
open boundary conditions, in which the sign of $\nu$ determines which edge.
Non-trivial topology manifests as directional amplification of a coherent input
with gain exponential in system size. Our work solves an outstanding problem in
the theory of NH topological phases and opens up new avenues in topological
photonics.
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quant-ph
|
Constructions of Unextendible Maximally Entangled Bases in \(\mathbb
{C}^{d}\otimes \mathbb {C}^{d^{\prime}}\): We study unextendible maximally entangled bases (UMEBs) in \(\mathbb
{C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) ($d<d'$). An operational method to
construct UMEBs containing $d(d^{\prime}-1)$ maximally entangled vectors is
established, and two UMEBs in \(\mathbb {C}^{5}\otimes \mathbb {C}^{6}\) and
\(\mathbb {C}^{5}\otimes \mathbb {C}^{12}\) are given as examples. Furthermore,
a systematic way of constructing UMEBs containing $d(d^{\prime}-r)$ maximally
entangled vectors in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\) is
presented for $r=1,2,\cdots, d-1$. Correspondingly, two UMEBs in \(\mathbb
{C}^{3}\otimes \mathbb {C}^{10}\) are obtained.
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quant-ph
|
Scalable design of tailored soft pulses for coherent control: We present a scalable scheme to design optimized soft pulses and pulse
sequences for coherent control of interacting quantum many-body systems. The
scheme is based on the cluster expansion and the time dependent perturbation
theory implemented numerically. This approach offers a dramatic advantage in
numerical efficiency, and it is also more convenient than the commonly used
Magnus expansion, especially when dealing with higher order terms. We
illustrate the scheme by designing 2nd-order pi-pulses and a 6th-order 8-pulse
refocusing sequence for a chain of qubits with nearest-neighbor couplings. We
also discuss the performance of soft-pulse refocusing sequences in suppressing
decoherence due to low-frequency environment.
|
quant-ph
|
Atomic Fock states by gradual trap reduction: from sudden to adiabatic
limits: We investigate the possibility to form high fidelity atomic Fock states by
gradual reduction of a quasi one dimensional trap containing spin polarized
fermions or strongly interacting bosons in the Tonk-Girardeau regime. Making
the trap shallower and simultaneously squeezing it can lead to the preparation
of an ideal atomic Fock state as one approaches either the sudden or the
adiabatic limits. Nonetheless, the fidelity of the resulting state is shown to
exhibit a non-monotonic behaviour with the time scale in which the trapping
potential is changed.
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quant-ph
|
Satellite-Based Quantum Key Distribution in the Presence of Bypass
Channels: The security of prepare-and-measure satellite-based quantum key distribution
(QKD), under restricted eavesdropping scenarios, is addressed. We particularly
consider cases where the eavesdropper, Eve, has limited access to the
transmitted signal by Alice, and/or Bob's receiver station. This restriction is
modeled by lossy channels between Alice/Bob and Eve, where the transmissivity
of such channels can, in principle, be bounded by monitoring techniques. An
artefact of such lossy channels is the possibility of having {\it bypass}
channels, those which are not accessible to Eve, but may not necessarily be
characterized by the users either. This creates interesting, unexplored,
scenarios for analyzing QKD security. In this paper, we obtain generic bounds
on the key rate in the presence of bypass channels and apply them to
continuous-variable QKD protocols with Gaussian encoding with direct and
reverse reconciliation. We find regimes of operation in which the above
restrictions on Eve can considerably improve system performance. We also
develop customised bounds for several protocols in the BB84 family and show
that, in certain regimes, even the simple protocol of BB84 with weak coherent
pulses is able to offer positive key rates at high channel losses, which would
otherwise be impossible under an unrestricted Eve. In this case the limitation
on Eve would allow Alice to send signals with larger intensities than the
optimal value under an ideal Eve, which effectively reduces the effective
channel loss. In all these cases, the part of the transmitted signal that does
not reach Eve can play a non-trivial role in specifying the achievable key
rate. Our work opens up new security frameworks for spaceborne quantum
communications systems.
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quant-ph
|
Universal approach for quantum interfaces with atomic arrays: We develop a general approach for the characterization of atom-array
platforms as light-matter interfaces, focusing on their application in quantum
memory and photonic entanglement generation. Our approach is based on the
mapping of atom-array problems to a generic 1D model of light interacting with
a collective dipole. We find that the efficiency of light-matter coupling,
which in turn determines those of quantum memory and entanglement, is given by
the on-resonance reflectivity of the 1D scattering problem, $r_0=C/(1+C)$,
where $C$ is a cooperativity parameter of the model. For 2D and 3D atomic
arrays in free space, we derive the mapping parameter $C$ and hence $r_0$,
while accounting for realistic effects such as the finite sizes of the array
and illuminating beam and weak disorder in atomic positions. Our analytical
results are verified numerically and reveal a key idea: efficiencies of quantum
tasks are reduced by our approach to the classical calculation of a
reflectivity. This provides a unified framework for the analysis of collective
light-matter coupling in various relevant platforms such as optical lattices
and tweezer arrays. Generalization to collective systems beyond arrays is
discussed.
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quant-ph
|
Entanglement Production and Convergence Properties of the Variational
Quantum Eigensolver: We perform a systematic investigation of variational forms (wave function
Ans\"atze), to determine the ground state energies and properties of
two-dimensional model fermionic systems on triangular lattices (with and
without periodic boundary conditions), using the Variational Quantum
Eigensolver (VQE) algorithm. In particular, we focus on the nature of the
entangler blocks which provide the most efficient convergence to the system
ground state inasmuch as they use the minimal number of gate operations, which
is key for the implementation of this algorithm in NISQ computers. Using the
concurrence measure, the amount of entanglement of the register qubits is
monitored during the entire optimization process, illuminating its role in
determining the efficiency of the convergence. Finally, we investigate the
scaling of the VQE circuit depth as a function of the desired energy accuracy.
We show that the number of gates required to reach a solution within an error
$\varepsilon$ follows the Solovay-Kitaev scaling,
$\mathcal{O}(\log^c(1/\varepsilon))$, with an exponent $c = 1.31
{\rm{\pm}}0.13$.
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quant-ph
|
Gauge transformations for a driven quantum particle in an infinite
square well: Quantum mechanics of a particle in an infinite square well under the
influence of a time-dependent electric field is reconsidered. In some gauge,
the Hamiltonian depends linearly on the momentum operator which is symmetric
but not self-adjoint when defined on a finite interval. In spite of this
symmetric part, the Hamiltonian operator is shown to be self-adjoint. This
follows from a theorem by Kato and Rellich which guarantees the stability of a
self-adjoint operator under certain symmetric perturbations. The result, which
has been assumed tacitly by other authors, is important in order to establish
the equivalence of different Hamiltonian operators related to each other by
quantum gauge transformations. Implications for the quantization procedure of a
particle in a box are pointed out.
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quant-ph
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Anneal-path correction in flux qubits: Quantum annealers require accurate control and optimized operation schemes to
reduce noise levels, in order to eventually demonstrate a computational
advantage over classical algorithms. We study a high coherence four-junction
capacitively shunted flux qubit (CSFQ), using dispersive measurements to
extract system parameters and model the device. Josephson junction asymmetry
inherent to the device causes a deleterious nonlinear cross-talk when annealing
the qubit. We implement a nonlinear annealing path to correct the asymmetry
in-situ, resulting in a substantial increase in the probability of the qubit
being in the correct state given an applied flux bias. We also confirm the
multi-level structure of our CSFQ circuit model by annealing it through small
spectral gaps and observing quantum signatures of energy level crossings. Our
results demonstrate an anneal-path correction scheme designed and implemented
to improve control accuracy for high-coherence and high-control quantum
annealers, which leads to an enhancement of success probability in annealing
protocols.
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quant-ph
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Pulsed multireservoir engineering for a trapped ion with applications to
state synthesis and quantum Otto cycles: Conducting an open quantum system towards a desired steady state through
reservoir engineering is a remarkable task that takes dissipation and
decoherence as tools rather than impediments. Here we develop a collisional
model to implement reservoir engineering for the one-dimensional harmonic
motion of a trapped ion. Our scheme is based on the pulsed interaction between
the vibrational mode and the electronic levels of a trapped ion, which is
promoted by resolved-sideband lasers. Having multiple internal levels, we show
that multiple reservoirs can be engineered, allowing for more efficient
synthesis of well-known non-classical states of motion and the generation of
states that are unfeasible with a single-bath setup, for instance, thermal
states with arbitrary positive temperatures. We apply these ideas to quantum
Otto cycles beyond purely thermal reservoirs. In particular, we present general
conditions for the violation of the standard Otto bound in the limiting regime
of non-adiabatic dynamics.
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quant-ph
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Channel and carrier adapted quantum error correction: The paper has been withdrawn by the autors. The proposed code is not working
because orthogonality.
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quant-ph
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Measurement-device-independent quantum key distribution with quantum
memories: We generalize measurement-device-independent quantum key distribution [ H.-K.
Lo, M. Curty, and B. Qi, Phys. Rev. Lett. 108, 130503 (2012) ] to the scenario
where the Bell-state measurement station contains also heralded quantum
memories. We find analytical formulas, in terms of device imperfections, for
all quantities entering in the secret key rates, i.e., the quantum bit error
rate and the repeater rate. We assume either single-photon sources or weak
coherent pulse sources plus decoy states. We show that it is possible to
significantly outperform the original proposal, even in presence of decoherence
of the quantum memory. Our protocol may represent the first natural step for
implementing a two-segment quantum repeater.
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quant-ph
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QuGeo: An End-to-end Quantum Learning Framework for Geoscience -- A Case
Study on Full-Waveform Inversion: The rapid advancement of quantum computing has generated considerable
anticipation for its transformative potential. However, harnessing its full
potential relies on identifying "killer applications". In this regard, QuGeo
emerges as a groundbreaking quantum learning framework, poised to become a key
application in geoscience, particularly for Full-Waveform Inversion (FWI). This
framework integrates variational quantum circuits with geoscience, representing
a novel fusion of quantum computing and geophysical analysis. This synergy
unlocks quantum computing's potential within geoscience. It addresses the
critical need for physics-guided data scaling, ensuring high-performance
geoscientific analyses aligned with core physical principles. Furthermore,
QuGeo's introduction of a quantum circuit custom-designed for FWI highlights
the critical importance of application-specific circuit design for quantum
computing. In the OpenFWI's FlatVelA dataset experiments, the variational
quantum circuit from QuGeo, with only 576 parameters, achieved significant
improvement in performance. It reached a Structural Similarity Image Metric
(SSIM) score of 0.905 between the ground truth and the output velocity map.
This is a notable enhancement from the baseline design's SSIM score of 0.800,
which was achieved without the incorporation of physics knowledge.
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quant-ph
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Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic
simulation: Simulators can realise novel phenomena by separating them from the
complexities of a full physical implementation. Here we put forward a scheme
that can simulate the exotic statistics of $D(S_3)$ non-Abelian anyons with
minimal resources. The qudit lattice representation of this planar code
supports local encoding of $D(S_3)$ anyons. As a proof-of-principle
demonstration we employ a photonic simulator to encode a single qutrit and
manipulate it to perform the fusion and braiding properties of non-Abelian
$D(S_3)$ anyons. The photonic technology allows us to perform the required
non-unitary operations with much higher fidelity than what can be achieved with
current quantum computers. Our approach can be directly generalised to larger
systems or to different anyonic models, thus enabling advances in the
exploration of quantum error correction and fundamental physics alike.
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quant-ph
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Quantum reading capacity: General definition and bounds: Quantum reading refers to the task of reading out classical information
stored in a read-only memory device. In any such protocol, the transmitter and
receiver are in the same physical location, and the goal of such a protocol is
to use these devices (modeled by independent quantum channels), coupled with a
quantum strategy, to read out as much information as possible from a memory
device, such as a CD or DVD. As a consequence of the physical setup of quantum
reading, the most natural and general definition for quantum reading capacity
should allow for an adaptive operation after each call to the channel, and this
is how we define quantum reading capacity in this paper. We also establish
several bounds on quantum reading capacity, and we introduce an
environment-parametrized memory cell with associated environment states,
delivering second-order and strong converse bounds for its quantum reading
capacity. We calculate the quantum reading capacities for some exemplary memory
cells, including a thermal memory cell, a qudit erasure memory cell, and a
qudit depolarizing memory cell. We finally provide an explicit example to
illustrate the advantage of using an adaptive strategy in the context of
zero-error quantum reading capacity.
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quant-ph
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Concurrence for multipartite states: We construct a generalized concurrence for general multipartite states based
on local W-class and GHZ-class operators. We explicitly construct the
corresponding concurrence for three-partite states. The construction of the
concurrence is interesting since it is based on local operators.
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quant-ph
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Dynamical suppression of tunneling and spin switching of a
spin-orbit-coupled atom in a double-well trap: We predict wide-band suppression of tunneling of spin-orbit-coupled atoms (or
noninteracting Bose-Einstein condensate) in a double-well potential with
periodically varying depths of the potential wells. The suppression of
tunneling is possible for a single state and for superposition of two states,
i.e. for a qbit. By varying spin-orbit coupling one can drastically increase
the range of modulation frequencies in which an atom remains localized in one
of the potential wells, the effect connected with crossing of energy levels.
This range of frequencies is limited because temporal modulation may also
excite resonant transitions between lower and upper states in different wells.
The resonant transitions enhance tunneling and are accompanied by pseudo-spin
switching. Since the frequencies of the resonant transitions are independent of
potential modulation depth, in contrast to frequencies at which suppression of
tunneling occurs, by varying this depth one can dynamically control both
spatial localization and pseudo-spin of the final state.
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quant-ph
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Uncertainties in Gapped Graphene: Motivated by graphene-based quantum computer we examine the time-dependence
of the position-momentum and position-velocity uncertainties in the monolayer
gapped graphene. The effect of the energy gap to the uncertainties is shown to
appear via the Compton-like wavelength $\lambda_c$. The uncertainties in the
graphene are mainly contributed by two phenomena, spreading and zitterbewegung.
While the former determines the uncertainties in the long-range of time, the
latter gives the highly oscillation to the uncertainties in the short-range of
time. The uncertainties in the graphene are compared with the corresponding
values for the usual free Hamiltonian $\hat{H}_{free} = (p_1^2 + p_2^2) / 2 M$.
It is shown that the uncertainties can be under control within the quantum
mechanical law if one can choose the gap parameter $\lambda_c$ freely.
|
quant-ph
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Casimir forces from a loop integral formulation: We reformulate the Casimir force in the presence of a non-trivial background.
The force may be written in terms of loop variables, the loop being a curve
around the scattering sites. A natural path ordering of exponentials take place
when a particular representation of the scattering centres is given. The basic
object to be evaluated is a reduced (or abbreviated) classical pseudo-action
that can be operator valued.
|
quant-ph
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Quantum metrology with a quantum-chaotic sensor: Quantum metrology promises high-precision measurements of classical
parameters with far reaching implications for science and technology. So far,
research has concentrated almost exclusively on quantum-enhancements in
integrable systems, such as precessing spins or harmonic oscillators prepared
in non-classical states. Here we show that large benefits can be drawn from
rendering integrable quantum sensors chaotic, both in terms of achievable
sensitivity as well as robustness to noise, while avoiding the challenge of
preparing and protecting large-scale entanglement. We apply the method to
spin-precession magnetometry and show in particular that the sensitivity of
state-of-the-art magnetometers can be further enhanced by subjecting the
spin-precession to non-linear kicks that renders the dynamics chaotic.
|
quant-ph
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Comparison of quantum state protection against decoherence via weak
measurement, a survey: One of the crucial tasks in quantum systems is to reduce the effects of
decoherence due to the unavoidable interactions between a system and its
environment. Many protection schemes have been proposed recently, among them
the weak measurement quantum measurement reversal (WMQMR), weak
measurement-based quantum feedback control (QFBC) and quantum feed-forward
control (QFFC) are reviewed in this paper. By considering weak measurement, the
aim is to find a balance between information gain and disturbance of the system
caused by the measurement. We classify different types of measurement and give
the definition of noise sources and their effects on the state of the system.
Finally, we compare and analyze the performance of the discussed protection
schemes for different noise sources by numerical simulations.
|
quant-ph
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Entangling metropolitan-distance separated quantum memories: Quantum internet gives the promise of getting all quantum resources
connected, and it will enable applications far beyond a localized scenario. A
prototype is a network of quantum memories that are entangled and well
separated. Previous realizations are limited in the distance. In this paper, we
report the establishment of remote entanglement between two atomic quantum
memories physically separated by 12.5 km directly in a metropolitan area. We
create atom-photon entanglement in one node and send the photon to a second
node for storage. We harness low-loss transmission through a field-deployed
fiber of 20.5 km by making use of frequency down-conversion and up-conversion.
The final memory-memory entanglement is verified to have a fidelity of 90% via
retrieving to photons. Our experiment paves the way to study quantum network
applications in a practical scenario.
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quant-ph
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Stationary measure for two-state space-inhomogeneous quantum walk in one
dimension: We consider the two-state space-inhomogeneous coined quantum walk (QW) in one
dimension. For a general setting, we obtain the stationary measure of the QW by
solving the eigenvalue problem. As a corollary, stationary measures of the
multi-defect model and space-homogeneous QW are derived. The former is a
generalization of the previous works on one-defect model and the latter is a
generalization of the result given by Konno and Takei (2015).
|
quant-ph
|
Random Quantum Circuits and Pseudo-Random Operators: Theory and
Applications: Pseudo-random operators consist of sets of operators that exhibit many of the
important statistical features of uniformly distributed random operators. Such
pseudo-random sets of operators are most useful whey they may be parameterized
and generated on a quantum processor in a way that requires exponentially fewer
resources than direct implementation of the uniformly random set. Efficient
pseudo-random operators can overcome the exponential cost of random operators
required for quantum communication tasks such as super-dense coding of quantum
states and approximately secure quantum data-hiding, and enable efficient
stochastic methods for noise estimation on prototype quantum processors. This
paper summarizes some recently published work demonstrating a random circuit
method for the implementation of pseudo-random unitary operators on a quantum
processor [Emerson et al., Science 302:2098 (Dec.~19, 2003)], and further
elaborates the theory and applications of pseudo-random states and operators.
|
quant-ph
|
Resource theory of dephasing estimation in multiqubit systems: We present a resource theory to investigate the power of a multqubit system
as a probe in the task of dephasing estimation. Our approach employs the
quantum Fisher information about the dephasing parameter as the resource
measure. Based on the monotonicity of quantum Fisher information, we propose
two sets of free operations in our resource theory, the Hamming distance
preserving operations and the selectively Hamming distance preserving
operations. We derive a necessary condition for the state transformation under
these free operations and demonstrate that uniform superposition states are the
golden states in our resource theory. We further compare our resource theory
with the resource theory of coherence and thoroughly investigate the relation
between their free operations in both single-qubit and multiqubit cases.
Additionally, for multiqubit systems, we discover the incompatibility between
the resource theory of dephasing estimation and that of $U(1)$ asymmetry, which
is responsible for phase estimation. The condition for enhancing the
performance of a probe state in phase estimation while preserving its ability
in dephasing estimation is also discussed. Our results provide new insights
into quantum parameter estimation by the resource-theoretic approach.
|
quant-ph
|
Finite geometry models of electric field noise from patch potentials in
ion traps: We model electric field noise from fluctuating patch potentials on conducting
surfaces by taking into account the finite geometry of the ion trap electrodes
to gain insight into the origin of anomalous heating in ion traps. The scaling
of anomalous heating rates with surface distance, $d$, is obtained for several
generic geometries of relevance to current ion trap designs, ranging from
planar to spheroidal electrodes. The influence of patch size is studied both by
solving Laplace's equation in terms of the appropriate Green's function as well
as through an eigenfunction expansion. Scaling with surface distance is found
to be highly dependent on the choice of geometry and the relative scale between
the spatial extent of the electrode, the ion-electrode distance, and the patch
size. Our model generally supports the $d^{-4}$ dependence currently found by
most experiments and models, but also predicts geometry-driven deviations from
this trend.
|
quant-ph
|
Entanglement dynamics in dissipative photonic Mott insulators: We theoretically investigate the entanglement dynamics in photonic Mott
insulators in the presence of particle losses and dephasing. We explore two
configurations where entanglement is generated following the injection or
extraction of a photon in the central site of a chain of cavity resonators. We
study the entanglement negativity of two-site reduced density matrices as a
function of time and inter-site distance. Our findings show that in spite of
particle losses the quantum entanglement propagation exhibits a ballistic
character with propagation speeds related to the differerent quasiparticles
that are involved in the dynamics, namely photonic doublons and holons
respectively. Our analysis reveals that photon dissipation has a strikingly
asymmetric behavior in the two configurations with a much more dramatic role on
the holon entanglement propagation than for the doublon case.
|
quant-ph
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A new proof for the existence of mutually unbiased bases: We develop a strong connection between maximally commuting bases of
orthogonal unitary matrices and mutually unbiased bases. A necessary condition
of the existence of mutually unbiased bases for any finite dimension is
obtained. Then a constructive proof of the existence of mutually unbiased bases
for dimensions which are power of a prime is presented. It is also proved that
in any dimension d the number of mutually unbiased bases is at most d+1. An
explicit representation of mutually unbiased observables in terms of Pauli
matrices are provided for d=2^m.
|
quant-ph
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Quantum analog of resource theory of stinginess: We present a resource theory of stinginess, first in a classical scenario,
and then, point to a possible quantum version of the same.
|
quant-ph
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Single photon reflection and transmission in optomechanical system: Cavity Optomechanical system is speedily approaching the regime where the
radiation pressure of a single photon displaces the moving mirror. In this
paper, we consider a cavity optomechanical system where the cavity field is
driven by an external field. In the limit of weak mirror-cavity couplings, we
calculate analytically the reflection and transmission rates for cavity field
and discuss the effects of mirror-cavity coupling on the reflection and
transmission.
|
quant-ph
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Fault-tolerant complexes: Fault-tolerant complexes describe surface-code fault-tolerant protocols from
a single geometric object. We first introduce fusion complexes that define a
general family of fusion-based quantum computing (FBQC) fault-tolerant quantum
protocols based on surface codes. We show that any 3-dimensional cell complex
where each edge has four incident faces gives a valid fusion complex. This
construction enables an automated search for fault tolerance schemes, allowing
us to identify 627 examples within a moderate search time. We implement this
using the open-source software tool Gavrog and present threshold results for a
variety of schemes, finding fusion networks with higher erasure and Pauli
thresholds than those existing in the literature. We then define more general
structures we call fault-tolerant complexes that provide a homological
description of fault tolerance from a large family of low-level error models,
which include circuit-based computation, floquet-based computation, and FBQC
with multi-qubit measurements. This extends the applicability of homological
descriptions of fault tolerance, and enables the generation of many new schemes
which have not been previously identified. We also define families of
fault-tolerant complexes for color codes and 3d single-shot subsystem codes,
which enables similar constructive methods, and we present several new examples
of each.
|
quant-ph
|
Quantum Walk Search on the Complete Bipartite Graph: The coined quantum walk is a discretization of the Dirac equation of
relativistic quantum mechanics, and it is the basis of many quantum algorithms.
We investigate how it searches the complete bipartite graph of $N$ vertices for
one of $k$ marked vertices with different initial states. We prove intriguing
dependence on the number of marked and unmarked vertices in each partite set.
For example, when the graph is irregular and the initial state is the typical
uniform superposition over the vertices, then the success probability can vary
greatly from one timestep to the next, even alternating between 0 and 1, so the
precise time at which measurement occurs is crucial. When the initial state is
a uniform superposition over the edges, however, the success probability
evolves smoothly. As another example, if the complete bipartite graph is
regular, then the two initial states are equivalent. Then if two marked
vertices are in the same partite set, the success probability reaches 1/2, but
if they are in different partite sets, it instead reaches $1$. This differs
from the complete graph, which is the quantum walk formulation of Grover's
algorithm, where the success probability with two marked vertices is 8/9. This
reveals a contrast to the continuous-time quantum walk, whose evolution is
governed by Schr\"odinger's equation, which asymptotically searches the regular
complete bipartite graph with any arrangement of marked vertices in the same
manner as the complete graph.
|
quant-ph
|
Creation of Two-Mode Squeezed States in Atomic Mechanical Oscillators: Two-mode squeezed states, which are entangled states with bipartite quantum
correlations in continuous-variable systems, are crucial in quantum information
processing and metrology. Recently, continuous-variable quantum computing with
the vibrational modes of trapped atoms has emerged with significant progress,
featuring a high degree of control in hybridizing with spin qubits. Creating
two-mode squeezed states in such a platform could enable applications that are
only viable with photons. Here, we experimentally demonstrate two-mode squeezed
states by employing atoms in a two-dimensional optical lattice as quantum
registers. The states are generated by a controlled projection conditioned on
the relative phase of two independent squeezed states. The individual squeezing
is created by sudden jumps of the oscillators' frequencies, allowing generating
of the two-mode squeezed states at a rate within a fraction of the oscillation
frequency. We validate the states by entanglement steering criteria and Fock
state analysis. Our results can be applied in other mechanical oscillators for
quantum sensing and continuous-variable quantum information.
|
quant-ph
|
Markovian semigroup from non-Markovian evolutions: It is shown that a convex combination of two non-Markovian evolutions may
lead to Markovian semigroup. This shows that convex combination of quantum
evolutions displaying nontrivial memory effects may result in a perfectly
memoryless evolution.
|
quant-ph
|
Attacks on quantum key distribution protocols that employ non-ITS
authentication: We demonstrate how adversaries with unbounded computing resources can break
Quantum Key Distribution (QKD) protocols which employ a particular message
authentication code suggested previously. This authentication code, featuring
low key consumption, is not Information-Theoretically Secure (ITS) since for
each message the eavesdropper has intercepted she is able to send a different
message from a set of messages that she can calculate by finding collisions of
a cryptographic hash function. However, when this authentication code was
introduced it was shown to prevent straightforward Man-In-The-Middle (MITM)
attacks against QKD protocols.
In this paper, we prove that the set of messages that collide with any given
message under this authentication code contains with high probability a message
that has small Hamming distance to any other given message. Based on this fact
we present extended MITM attacks against different versions of BB84 QKD
protocols using the addressed authentication code; for three protocols we
describe every single action taken by the adversary. For all protocols the
adversary can obtain complete knowledge of the key, and for most protocols her
success probability in doing so approaches unity.
Since the attacks work against all authentication methods which allow to
calculate colliding messages, the underlying building blocks of the presented
attacks expose the potential pitfalls arising as a consequence of non-ITS
authentication in QKD-postprocessing. We propose countermeasures, increasing
the eavesdroppers demand for computational power, and also prove necessary and
sufficient conditions for upgrading the discussed authentication code to the
ITS level.
|
quant-ph
|
A Fock state lattice approach to quantum optics: We analyze a set of models frequently appearing in quantum optical settings
by expressing their Hamiltonians in terms of Fock-state lattices. The few
degrees-of-freedom of such models, together with the system symmetries, make
the emerging Fock-state lattices rather simple such that they can be linked to
known lattice models from the condensed matter community. This sheds new light
on known quantum optical systems. While we provide a rather long list of models
and their corresponding Fock-state lattices, we pick a few ones in order to
demonstrate the strength of the method. The three-mode boson model, for
example, is shown to display a fractal spectrum, and chiral evolution in the
Fock-state lattice characterized by localized distributions traversing along
symmetric trajectories. In a second example we consider the central spin model
which generates a Fock-state lattice reminiscent of the SSH-model hosting
topological edge states. We further demonstrate how the phenomena of flat bands
in lattice models can manifest in related Fock-state lattices, which can be
linked to so called dark states.
|
quant-ph
|
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