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Quantum electromdynamics in a linear absorbing dielectric medium: The eletromagnetic field in a linear absorptive dielectric medium, is
quantized in the framework of the damped polarization model. A Hamiltonian
containing a reservoir with continuous degrees of freedom, is proposed. The
reservoir minimally interacts with the dielectric polarization and the
electromagnetic field. The Lagevin-Schrodinger equation is obtained as the
equation of motion of the polarization field. The radiation reaction
electromagnetic field is considered. For a homogeneous medium, the equations of
motion are solved using the Laplace transformation method. | quant-ph |
A better lower bound for quantum algorithms searching an ordered list: We show that any quantum algorithm searching an ordered list of n elements
needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries
are both necessary and sufficient. This shows that quantum algorithms can
achieve only a constant speedup for this problem. Our result improves lower
bounds of Buhrman and de Wolf(quant-ph/9811046) and Farhi, Goldstone, Gutmann
and Sipser (quant-ph/9812057). | quant-ph |
Generating a Schrödinger-cat-like state via a coherent superposition
of photonic operations: We propose an optical scheme to generate a superposition of coherent states
with enhanced size adopting an interferometric setting at the single-photon
level currently available in the laboratory. Our scheme employs a nondegenerate
optical parametric amplifier together with two beam splitters so that the
detection of single photons at the output conditionally implements the desired
superposition of second-order photonic operations. We analyze our proposed
scheme by considering realistic on-off photodetectors with nonideal efficiency
in heralding the success of conditional events. A high-quality performance of
our scheme is demonstrated in view of various criteria such as quantum
fidelity, mean output energy, and measure of quantum interference. | quant-ph |
Towards a Multi Target Quantum Computational Logic: Unlike the standard Quantum Computational Logic (QCL), where the carrier of
information (target) is conventionally assumed to be only the last qubit over a
sequence of many qubits, here we propose an extended version of the QCL (we
call Multi Target Quantum Computational Logic, briefly MTQCL) where the number
and the position of the target qubits are arbitrary. | quant-ph |
Identification of all Hardy-type correlations for two photons or
particles with spin 1/2: By using an alternative, equivalent form of the CHSH inequality and making
extensive use of the experimentally testable property of physical locality we
determine the 64 different Bell-type inequalities (each one involving four
joint probabilities) into which Hardy's nonlocality theorem can be cast. This
allows one to identify all the two-qubit correlations which can exhibit
Hardy-type nonlocality. | quant-ph |
Experimental implementation of universal holonomic quantum computation
on solid-state spins with optimal control: Experimental realization of a universal set of quantum logic gates with
high-fidelity is critical to quantum information processing, which is always
challenging by inevitable interaction between the quantum system and
environment. Geometric quantum computation is noise immune, and thus offers a
robust way to enhance the control fidelity. Here, we experimentally implement
the recently proposed extensible nonadiabatic holonomic quantum computation
with solid spins in diamond at room-temperature, which maintains both
flexibility and resilience against decoherence and system control errors.
Compared with previous geometric method, the fidelities of a universal set of
holonomic single-qubit and two-qubit quantum logic gates are improved in
experiment. Therefore, this work makes an important step towards fault-tolerant
scalable geometric quantum computation in realistic systems. | quant-ph |
Calculation of accurate permanent dipole moments of the lowest $^{1,3}
Σ^+$ states of heteronuclear alkali dimers using extended basis sets: The obtention of ultracold samples of dipolar molecules is a current
challenge which requires an accurate knowledge of their electronic properties
to guide the ongoing experiments. In this paper, we systematically investigate
the ground state and the lowest triplet state of mixed alkali dimers (involving
Li, Na, K, Rb, Cs) using a standard quantum chemistry approach based on
pseudopotentials for atomic core representation, gaussian basis sets, and
effective terms for core polarization effects. We emphasize on the convergence
of the results for permanent dipole moments regarding the size of the gaussian
basis set, and we discuss their predicted accuracy by comparing to other
theoretical calculations or available experimental values. We also revisit the
difficulty to compare computed potential curves among published papers, due to
the differences in the modelization of core-core interaction. | quant-ph |
Quantum Strategies for Rendezvous and Domination Tasks on Graphs with
Mobile Agents: This paper explores the application of quantum non-locality, a renowned and
unique phenomenon acknowledged as a valuable resource. Focusing on a novel
application, we demonstrate its quantum advantage for mobile agents engaged in
specific distributed tasks without communication. The research addresses the
significant challenge of rendezvous on graphs and introduces a new distributed
task for mobile agents grounded in the graph domination problem. Through an
investigation across various graph scenarios, we showcase the quantum
advantage. Additionally, we scrutinize deterministic strategies, highlighting
their comparatively lower efficiency compared to quantum strategies. The paper
concludes with a numerical analysis, providing further insights into our
findings. | quant-ph |
The Generalized Uncertainty Principle: The uncertainty principle lies at the heart of quantum physics, and is widely
thought of as a fundamental limit on the measurement precisions of incompatible
observables. Here we show that the traditional uncertainty relation in fact
belongs to the leading order approximation of a generalized uncertainty
relation. That is, the leading order linear dependence of observables gives the
Heisenberg type of uncertainty relations, while higher order nonlinear
dependence may reveal more different and interesting correlation properties.
Applications of the generalized uncertainty relation and the high order
nonlinear dependence between observables in quantum information science are
also discussed. | quant-ph |
Violation of Bell inequalities through the coincidence-time loophole: The coincidence-time loophole was identified by Larsson & Gill (Europhys.
Lett. 67, 707 (2004)); a concrete model that exploits this loophole has
recently been described by De Raedt et al. (Found. Phys., to appear). It is
emphasized here that De Raedt et al.'s model is experimentally testable. De
Raedt et al.'s model also introduces contextuality in a novel and classically
more natural way than the use of contextual particle properties, by introducing
a probabilistic model of a limited set of degrees of freedom of the measurement
apparatus, so that it can also be seen as a random field model. Even though De
Raedt et al.'s model may well contradict detailed Physics, it nonetheless
provides a way to simulate the logical operation of elements of a quantum
computer, and may provide a way forward for more detailed random field models. | quant-ph |
Updating the Born rule: Despite the tremendous empirical success of quantum theory there is still
widespread disagreement about what it can tell us about the nature of the
world. A central question is whether the theory is about our knowledge of
reality, or a direct statement about reality itself. Regardless of their stance
on this question, current interpretations of quantum theory regard the Born
rule as fundamental and add an independent state-update (or "collapse") rule to
describe how quantum states change upon measurement. In this paper we present
an alternative perspective and derive a probability rule that subsumes both the
Born rule and the collapse rule. We show that this more fundamental probability
rule can provide a rigorous foundation for informational, or "knowledge-based",
interpretations of quantum theory. | quant-ph |
Fluctuations of Energy-Relaxation Times in Superconducting Qubits: Superconducting qubits are an attractive platform for quantum computing since
they have demonstrated high-fidelity quantum gates and extensibility to modest
system sizes. Nonetheless, an outstanding challenge is stabilizing their
energy-relaxation times, which can fluctuate unpredictably in frequency and
time. Here, we use qubits as spectral and temporal probes of individual
two-level-system defects to provide direct evidence that they are responsible
for the largest fluctuations. This research lays the foundation for stabilizing
qubit performance through calibration, design, and fabrication. | quant-ph |
Adversarial quantum circuit learning for pure state approximation: Adversarial learning is one of the most successful approaches to modelling
high-dimensional probability distributions from data. The quantum computing
community has recently begun to generalize this idea and to look for potential
applications. In this work, we derive an adversarial algorithm for the problem
of approximating an unknown quantum pure state. Although this could be done on
universal quantum computers, the adversarial formulation enables us to execute
the algorithm on near-term quantum computers. Two parametrized circuits are
optimized in tandem: One tries to approximate the target state, the other tries
to distinguish between target and approximated state. Supported by numerical
simulations, we show that resilient backpropagation algorithms perform
remarkably well in optimizing the two circuits. We use the bipartite
entanglement entropy to design an efficient heuristic for the stopping
criterion. Our approach may find application in quantum state tomography. | quant-ph |
Atom-wall dispersive forces from master equation formalism: Using the general expressions for level shifts obtained from the master
equation for a small system interacting with a large one considered as a
reservoir, we calculate the dispersive potentials between an atom and a wall in
the dipole approximation. We analyze in detail the particular case of a
two-level atom in the presence of a perfectly conducting wall. We study the van
der Waals as well as the resonant interactions. All distance regimes as well as
the high and low temperature regimes are considered. We show that the
Casimir-Polder interaction can not be considered as a direct result of the
vacuum fluctuations only. Concerning the interaction between the atom and the
wall at high temperature, which show that a saturation of the potential for all
distances occurs. This saturated potential coincides exactly with that obtained
in the London-van der Waals limit. | quant-ph |
Algorithmic cooling for resolving state preparation and measurement
errors in quantum computing: State preparation and measurement errors are commonly regarded as
indistinguishable. The problem of distinguishing state preparation (SPAM)
errors from measurement errors is important to the field of characterizing
quantum processors. In this work, we propose a method to separately
characterize SPAM errors using a novel type of algorithmic cooling protocol
called measurement-based algorithmic cooling (MBAC). MBAC assumes the ability
to perform (potentially imperfect) projective measurements on individual
qubits, which is available on many modern quantum processors. We demonstrate
that MBAC can significantly reduce state preparation error under realistic
assumptions, with a small overhead that can be upper bounded by measurable
quantities. Thus, MBAC can be a valuable tool not only for benchmarking
near-term quantum processors, but also for improving the performance of quantum
processors in an algorithmic manner. | quant-ph |
Entanglement sharing among qudits: Consider a system consisting of n d-dimensional quantum particles (qudits),
and suppose that we want to optimize the entanglement between each pair. One
can ask the following basic question regarding the sharing of entanglement:
what is the largest possible value Emax(n,d) of the minimum entanglement
between any two particles in the system? (Here we take the entanglement of
formation as our measure of entanglement.) For n=3 and d=2, that is, for a
system of three qubits, the answer is known: Emax(3,2) = 0.550. In this paper
we consider first a system of d qudits and show that Emax(d,d) is greater than
or equal to 1. We then consider a system of three particles, with three
different values of d. Our results for the three-particle case suggest that as
the dimension d increases, the particles can share a greater fraction of their
entanglement capacity. | quant-ph |
Quantum-state engineering in cavity magnomechanics formed by
two-dimensional magnetic materials: Cavity magnomechanics has become an ideal platform to explore macroscopic
quantum effects. Bringing together magnons, phonons, and photons in a system,
it opens many opportunities for quantum technologies. It was conventionally
realized by an yttrium iron garnet, which exhibits a parametric magnon-phonon
coupling $\hat{m}^\dag\hat{m}(\hat{b}^\dag+\hat{b})$, with $\hat{m}$ and
$\hat{b}$ being the magnon and phonon modes. Inspired by the recent realization
of two-dimensional (2D) magnets, we propose a cavity magnomechanical system
using a 2D magnetic material with both optical and magnetic drivings. It
features the coexisting photon-phonon radiation-pressure coupling and quadratic
magnon-phonon coupling $\hat{m}^\dag\hat{m}(\hat{b}^\dag+\hat{b})^2$ induced by
the magnetostrictive interaction. A stable squeezing of the phonon and bi- and
tri-partite entanglements among the three modes are generated in the regimes
with a suppressed phonon number. Compared with previous schemes, ours does not
require any extra nonlinear interaction and reservoir engineering and is robust
against the thermal fluctuation. Enriching the realization of cavity
magnomechanics, our system exhibits its superiority in quantum-state
engineering due to the versatile interactions enabled by its 2D feature. | quant-ph |
Macroscopic quantum damping in SQUID rings: The measurement process is introduced in the dynamics of Josephson devices
exhibiting quantum behaviour in a macroscopic degree of freedom. The
measurement is shown to give rise to a dynamical damping mechanism whose
experimental observability could be relevant to understand decoherence in
macroscopic quantum systems. | quant-ph |
String tension and area-law probed using quantum superposition: We propose a method for measuring the string tension in gauge theories, by
considering an interference effect of mesons, which is governed by a space-time
area law, due to confinement. Although it is only a gedanken experiment for
real elementary particles, in the context of quantum simulations of confining
gauge theories such an experiment can be realized. | quant-ph |
On the Complexity of Quantum Searching Using Complex Queries: We discuss the quantum search algorithm using complex queries that has
recently been published by Grover (quant-ph/9706005). We recall the algorithm
adding some details showing which complex query has to be evaluated. Based on
this version of the algorithm we discuss its complexity. | quant-ph |
Programmable quantum emitter formation in silicon: Silicon-based quantum emitters are candidates for large-scale qubit
integration due to their single-photon emission properties and potential for
spin-photon interfaces with long spin coherence times. Here, we demonstrate
local writing and erasing of selected light-emitting defects using fs laser
pulses in combination with hydrogen-based defect activation and passivation. By
selecting forming gas (N2/H2) during thermal annealing of carbon-implanted
silicon, we form Ci centers while passivating the more common G-centers. The Ci
center is a telecom S-band emitter with very promising spin properties that
consists of a single interstitial carbon atom in the silicon lattice. Density
functional theory calculations show that the Ci center brightness is enhanced
by several orders of magnitude in the presence of hydrogen. Fs-laser pulses
locally affect the passivation or activation of quantum emitters with hydrogen
and enable programmable quantum emitter formation in a qubit-by-design
paradigm. | quant-ph |
Relative entropy derivation of the uncertainty principle with quantum
side information: We give a simple proof of the uncertainty principle with quantum side
information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the
monotonicity of the relative entropy. Our proof shows that the entropic
uncertainty principle can be viewed as a data-processing inequality, a special
case of the notion that information cannot increase due to evolution in time.
This leads to a systematic method for finding the minimum uncertainty states of
various entropic uncertainty relations; interestingly such states are
intimately connected with the reversibility of time evolution. | quant-ph |
Quantum computation using arrays of N polar molecules in pendular states: We investigate several aspects of realizing quantum computation using
entangled polar molecules in pendular states. Quantum algorithms typically
start from a product state |00...0> and we show that up to a negligible error,
the ground states of polar molecule arrays can be considered as the unentangled
qubit basis state |00...0>. This state can be prepared by simply allowing the
system to reach thermal equilibrium at low temperature (<1 mK). We also
evaluate entanglement, characterized by the concurrence of pendular state
qubits in dipole arrays as governed by the external electric field,
dipole-dipole coupling and number N of molecules in the array. In the parameter
regime that we consider for quantum computing, we find that qubit entanglement
is modest, typically no greater than 0.0001, confirming the negligible
entanglement in the ground state. We discuss methods for realizing quantum
computation in the gate model, measurement based model, instantaneous quantum
polynomial time circuits and the adiabatic model using polar molecules in
pendular states. | quant-ph |
Low-depth simulations of fermionic systems on square-grid quantum
hardware: We present a general strategy for mapping fermionic systems to quantum
hardware with square qubit connectivity which yields low-depth quantum
circuits, counted in the number of native two-qubit fSIM gates. We achieve this
by leveraging novel operator decomposition and circuit compression techniques
paired with specifically chosen low-depth fermion-to-qubit mappings and allow
for a high degree of gate cancellations and parallelism. Our mappings retain
the flexibility to simultaneously optimize for qubit counts or qubit operator
weights and can be used to investigate arbitrary fermionic lattice geometries.
We showcase our approach by investigating the tight-binding model, the
Fermi-Hubbard model as well as the multi-orbital Hubbard-Kanamori model. We
report unprecedentedly low circuit depths per single Trotter layer with up to a
$70 \%$ improvement upon previous state-of-the-art. Our compression technique
also results in significant reduction of two-qubit gates. We find the lowest
gate-counts when applying the XYZ-formalism to the DK mapping. Additionally, we
show that our decomposition and compression formalism produces favourable
circuits even when no native parameterized two-qubit gates are available. | quant-ph |
Generalized Spherical Harmonics: We generalize the spherical harmonics for l=1 and give the differential
equation that the generalized forms satisfy. The new forms have an obvious
interpretation in the context of quantum mechanics. | quant-ph |
Relativistic Quantum Theory of Cyclotron Resonance in a Medium: In this paper the relativistic quantum theory of cyclotron resonance in an
arbitrary medium is presented. The quantum equation of motion for charged
particle in the field of plane electromagnetic wave and uniform magnetic field
in a medium is solved in the eikonal approximation. The probabilities of
induced multiphoton transitions between Landau levels in strong laser field is
calculated. | quant-ph |
Optimal measurement strategies for the trine states with arbitrary prior
probabilities: We investigate the optimal measurement strategy for state discrimination of
the trine ensemble of qubit states prepared with arbitrary prior probabilities.
Our approach generates the minimum achievable probability of error and also the
maximum confidence strategy. Although various cases with symmetry have been
considered and solution techniques put forward in the literature, to our
knowledge this is only the second such closed form, analytical, arbitrary
prior, example available for the minimum-error figure of merit, after the
simplest and well-known two-state example. | quant-ph |
Information theory of quantum systems with some hydrogenic applications: The information-theoretic representation of quantum systems, which
complements the familiar energy description of the density-functional and
wave-function-based theories, is here discussed. According to it, the internal
disorder of the quantum-mechanical non-relativistic systems can be quantified
by various single (Fisher information, Shannon entropy) and composite (e.g.
Cramer-Rao, LMC shape and Fisher-Shannon complexity) functionals of the
Schr\"odinger probability density. First, we examine these concepts and its
application to quantum systems with central potentials. Then, we calculate
these measures for hydrogenic systems, emphasizing their predictive power for
various physical phenomena. Finally, some recent open problems are pointed out. | quant-ph |
Loophole-free test of local realism via Hardy's violation: Bell's theorem states that quantum mechanical description on physical
quantity cannot be fully explained by local realistic theories, and lays solid
basis for various quantum information applications. Hardy's paradox is
celebrated to be the simplest form of Bell's theorem concerning its "All versus
Nothing" way to test local realism. However, due to experimental imperfections,
existing tests of Hardy's paradox require additional assumptions of
experimental systems, which constitute potential loopholes for faithfully
testing local realistic theories. Here, we experimentally demonstrate Hardy's
nonlocality through a photonic entanglement source. By achieving a detection
efficiency of $82.2\%$, a quantum state fidelity of $99.10\%$ and applying high
speed quantum random number generators for measurement setting switching, the
experiment is implemented in a loophole-free manner. During $6$ hours of
running, a strong violation of $P_{\text{Hardy}}=4.646\times 10^{-4}$ up to $5$
standard deviations is observed with $4.32\times 10^{9}$ trials. A null
hypothesis test shows that the results can be explained by local realistic
theories with an upper bound probability of $10^{-16348}$. These testing
results present affirmative evidence against local realism, and provide an
advancing benchmark for quantum information applications based on Hardy's
paradox. | quant-ph |
Non-Perturbative Renormalization Group Analysis of the Ohmic Quantum
Dissipation: We analyze quantum tunneling with the Ohmic dissipation by the
non-perturbative renormalization group method. We calculate the localization
susceptibility to evaluate the critical dissipation for the quantum-classical
transition, and find considerably larger critical dissipation compared to the
previous semi-classical arguments. | quant-ph |
Efimov Physics: a review: This article reviews theoretical and experimental advances in Efimov physics,
an array of quantum few-body and many-body phenomena arising for particles
interacting via short-range resonant interactions, that is based on the
appearance of a scale-invariant three-body attraction theoretically discovered
by Vitaly Efimov in 1970. This three-body effect was originally proposed to
explain the binding of nuclei such as the triton and the Hoyle state of
carbon-12, and later considered as a simple explanation for the existence of
some halo nuclei. It was subsequently evidenced in trapped ultra-cold atomic
clouds and in diffracted molecular beams of gaseous helium. These experiments
revealed that the previously undetermined three-body parameter introduced in
the Efimov theory to stabilise the three-body attraction typically scales with
the range of atomic interactions. The few- and many-body consequences of the
Efimov attraction have been since investigated theoretically, and are expected
to be observed in a broader spectrum of physical systems. | quant-ph |
Measurements with prediction and retrodiction on the collective spin of
10^{11} atoms beat the standard quantum limit: Quantum probes using $N$ uncorrelated particles give a limit on the
measurement sensitivity referred to as the standard quantum limit (SQL). The
SQL, however, can be overcome by exploiting quantum entangled states, such as
spin squeezed states. We report generation of a quantum state, that surpasses
the SQL for probing of the collective spin of $10^{11}$ $\text{Rb}$ atoms
contained in a vapor cell. The state is prepared and verified by sequences of
stroboscopic quantum non-demolition (QND) measurements, and we apply the theory
of past quantum states to obtain the spin state information from the outcomes
of both earlier and later QND measurements. In this way, we obtain a
conditional noise reduction of 5.6 dB, and a metrologically-relevant squeezing
of $4.5\pm0.40~\text{dB}$. The past quantum state yields tighter information on
the spin component than we can obtain by a conventional QND measurement. Our
squeezing results are obtained with 1000 times more atoms than in any previous
experiments with a corresponding record $4.6\times10^{-13} rad^2$ variance of
the angular fluctuations of a squeezed collective spin. | quant-ph |
Quantum Interference, Hidden Symmetries: Theory and Experimental Facts: The concept of quantum superposition is reconsidered and discussed from the
viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum
mechanics, in order to elucidate some physical consequences that go beyond the
simple mathematical idea of linearly combining vectors in a Hilbert space.
Specifically, the discussion turns around the connection between symmetries
characterizing the wave function and the behavior in time displayed by the
quantum flux when the latter is analyzed in terms of streamlines (Bohmian
trajectories). This is illustrated with a series of analytical results and
numerical simulations, which include Young's two-slit experiment,
counter-propagating wave packets, grating diffraction and quantum carpets
(e.g., Talbot carpets), and diffraction under confinement conditions. From the
analysis presented it follows that quantum paradoxes appear whenever symmetries
related to interference are neglected in the interpretation and understanding
of the corresponding phenomena. | quant-ph |
All Optical Quantum Teleportation: We propose an all optical, continuous variable, quantum teleportation scheme
based on optical parametric amplifiers. | quant-ph |
Quantum probing topological phase transitions by non-Markovianity: Understanding the physical significance and probing the global invariants
characterizing quantum topological phases in extended systems is a main
challenge in modern physics with major impact in different areas of science.
Here, a quantum-information-inspired probing method is proposed where
topological phase transitions are revealed by a non-Markovianity quantifier.
The idea is illustrated by considering the decoherence dynamics of an external
read-out qubit that probes a Su-Schrieffer-Heeger (SSH) chain with either pure
dephasing or dissipative coupling. Qubit decoherence features and
non-Markovianity measure clearly signal the topological phase transition of the
SSH chain. | quant-ph |
Intertwining of exactly solvable generalized Schrodinger equations: The Darboux transformation operator technique in differential and integral
forms is applied to the generalized Schrodinger equation with a
position-dependent effective mass and with linearly energy-dependent
potentials. Intertwining operators are obtained in an explicit form and used
for constructing generalized Darboux transformations of an arbitrary order. A
relation between supersymmetry and the generalized Darboux transformation is
considered. The method is applied to generation of isospectral potentials with
additional or removal bound states or construction of new partner potentials
without changing the spectrum, i.e. fully isospectral potentials. The method is
illustrated by some examples. | quant-ph |
Quantum Mechanical Heat Transport in Disordered Harmonic Chains: We investigate the mechanism of heat conduction in ordered and disordered
harmonic onedimensional chains within the quantum mechanical Langevin method.
In the case of the disordered chains we find indications for normal heat
conduction which means that there is a finite temperature gradient but we
cannot clearly decide whether the heat resistance increases linearly with the
chain length. Furthermore we observe characteristic quantum mechanical features
like Bose-Einstein statistics of the occupation numbers of the normal modes,
freezing of the heat conductivity and the influence of the entanglement within
the chain on the current. For the ordered chain we recover some classical
results like a vanishing temperature gradient and a heat flux independent of
the length of the chain. | quant-ph |
Controlling a d-level atom in a cavity: In this paper we study controllability of a $d$-level atom interacting with
the electromagnetic field in a cavity. The system is modelled by an ordered
graph $\Gamma$. The vertices of $\Gamma$ describe the energy levels and the
edges allowed transitions. To each edge of $\Gamma$ we associate a harmonic
oscillator representing one mode of the electromagnetic field. The dynamics of
the system (drift) is given by a natural generalization of the Jaynes-Cummings
Hamiltonian. If we add in addition sufficient control over the atom, the
overall system (atom and em-field) becomes strongly controllable, i.e. each
unitary on the system Hilbert space can be approximated with arbitrary
precision in the strong topology by control unitaries. A key role in the proof
is played by a topological *-algebra which is (roughly speaking) a
representation of the path algebra of $\Gamma$. It contains crucial structural
information about the control problem, and is therefore an important tool for
the implementation of control tasks like preparing a particular state from the
ground state. This is demonstrated by a detailed discussion of different
versions of three-level systems. | quant-ph |
Multi-mode quantum correlation generated from an unbalanced SU(1,1)
interferometer using ultra-short laser pulses as pump: Multi-mode entanglement is one of the critical resource in quantum
information technology. Generating large scale multi-mode entanglement state by
coherently combining time-delayed continuous variables Einstein-Podolsky-Rosen
pairs with linear beam-splitters has been widely studied recently. Here we
theoretically investigate the multi-mode quantum correlation property of the
optical fields generated from an unbalanced SU(1,1) interferometer pumped
ultra-short pulses, which generates multi-mode entangled state by using a
non-degenerate parametric processes to coherently combine delayed
Einstein-Podolsky-Rosen pairs in different frequency band. The covariance
matrix of the generated multi-mode state is derived analytically for arbitrary
mode number $M$ within adjacent timing slot, which shows a given mode is
maximally correlated to 5 other modes. Based on the derived covariance matrix,
both photon number correlation and quadrature amplitude correlation of the
generated state is analyzed. We also extend our analyzing method to the scheme
of generating entangled state by using linear beam splitter as a coherent
combiner of delayed EPR pairs, and compare the states generated by the two
coherently combining schemes. Our result provides a comprehensive theoretical
description on the quantum correlations generated from an unbalanced SU(1,1)
interferometer within Gaussian system range, and will offer more perspectives
to quantum information technology. | quant-ph |
Implications of Electronics Constraints for Solid-State Quantum Error
Correction and Quantum Circuit Failure Probability: In this paper we present the impact of classical electronics constraints on a
solid-state quantum dot logical qubit architecture. Constraints due to routing
density, bandwidth allocation, signal timing, and thermally aware placement of
classical supporting electronics significantly affect the quantum error
correction circuit's error rate. We analyze one level of a quantum error
correction circuit using nine data qubits in a Bacon-Shor code configured as a
quantum memory. A hypothetical silicon double quantum dot quantum bit (qubit)
is used as the fundamental element. A pessimistic estimate of the error
probability of the quantum circuit is calculated using the total number of
gates and idle time using a provably optimal schedule for the circuit
operations obtained with an integer program methodology. The micro-architecture
analysis provides insight about the different ways the electronics impact the
circuit performance (e.g., extra idle time in the schedule), which can
significantly limit the ultimate performance of any quantum circuit and
therefore is a critical foundation for any future larger scale architecture
analysis. | quant-ph |
Exact solutions for a universal set of quantum gates on a family of
iso-spectral spin chains: We find exact solutions for a universal set of quantum gates on a scalable
candidate for quantum computers, namely an array of two level systems. The
gates are constructed by a combination of dynamical and geometrical
(non-Abelian) phases. Previously these gates have been constructed mostly on
non-scalable systems and by numerical searches among the loops in the manifold
of control parameters of the Hamiltonian. | quant-ph |
Interferometric Tests of Teleportation: We investigate a direct test of teleportation efficacy based on a
Mach-Zehnder interferometer. The analysis is performed for continuous variable
teleportation of both discrete and continuous observables. | quant-ph |
The scaling of boson sampling experiments: Boson sampling is the problem of generating a quantum bit stream whose
average is the permanent of a $n\times n$ matrix. The bitstream is created as
the output of a prototype quantum computing device with $n$ input photons. It
is a fundamental challenge to verify boson sampling, and the question of how
output count rates scale with matrix size $n$ is crucial. Here we apply results
from random matrix theory to establish scaling laws for average count rates in
boson sampling experiments with arbitrary inputs and losses. The results show
that, even with losses included, verification of nonclassical behaviour at
large $n$ values is indeed possible. | quant-ph |
A high fidelity heralded squeezing gate: A universal squeezing gate capable of squeezing arbitrary input states is
essential for continuous-variable quantum
computation~\cite{PRA79062318,PRL112120504}. However, in present
state-of-the-art techniques~\cite{PRA90060302,PRL106240504}, the fidelity of
such gates is ultimately limited by the need to create squeezed vacuum modes of
unbounded energy. Here we circumvent this fundamental limitation by using a
heralded squeezing gate. We propose and experimentally demonstrate a squeezing
gate that can achieve near unit fidelity for coherent input states. In
particular, for a target squeezing of \SI{2.3}{\dB}, we report a fidelity of
\SI{98.5}{\%}. This result cannot be reproduced by conventional schemes even if
the currently best available squeezing of \SI{15}{\dB}~\cite{PRL117110801} is
utilised when benchmarked on identical detection inefficiencies. Our technique
can be applied to non-Gaussian states and provides a promising pathway towards
high-fidelity gate operations and fault-tolerant quantum computation. | quant-ph |
Field-gradient measurement using a Stern-Gerlach atomic interferometer
with butterfly geometry: Atomic interferometers have been studied as a promising device for precise
sensing of external fields. Among various configurations, a particular
configuration with a butterfly-shaped geometry has been designed to sensitively
probe field gradients. We introduce a Stern-Gerlach (SG) butterfly
interferometer by incorporating magnetic field in the conventional
butterfly-shaped configuration. Atomic trajectories of the interferometer can
be flexibly adjusted by controlling magnetic fields to increase the sensitivity
of the interferometer, while the conventional butterfly interferometer using
Raman transitions can be understood as a special case. We also show that the SG
interferometer can keep high contrast against a misalignment in position and
momentum caused by the field gradient. | quant-ph |
A comment on the paper "How can a Result of a Single Coin Toss Turn Out
to be 100 Heads" by C. Ferrie and J. Combes: The authors of a recent paper [Phys. Rev. Lett. 113, 120404 (2014)] suggest
that "weak values are not inherently quantum but rather a purely statistical
feature of pre- and postselection with disturbance". We argue that this claim
is erroneous, since such values require averaging with distributions which
change sign. This type of averaging arises naturally in quantum mechanics, but
may not occur in classical statistics. | quant-ph |
Out-of-time-order correlators and quantum phase transitions in the Rabi
and Dicke model: The out-of-time-order correlators (OTOCs) is used to study the quantum phase
transitions (QPTs) between the normal phase and the superradiant phase in the
Rabi and few-body Dicke models with large frequency ratio of theatomic level
splitting to the single-mode electromagnetic radiation field frequency. The
focus is on the OTOC thermally averaged with infinite temperature, which is an
experimentally feasible quantity. It is shown that thecritical points can be
identified by long-time averaging of the OTOC via observing its local minimum
behavior. More importantly, the scaling laws of the OTOC for QPTs are revealed
by studying the experimentally accessible conditions with finite frequency
ratio and finite number of atoms in the studied models. The critical exponents
extracted from the scaling laws of OTOC indicate that the QPTs in the Rabi and
Dicke models belong to the same universality class. | quant-ph |
Anomalous Decay and Decoherence in Atomic Gases: Pair collisions in atomic gases lead to decoherence and decay. Assuming that
all the atoms in the gas are equally likely to collide one is led to consider
Lindbladian of mean field type where the evolution in the limit of many atoms
reduces to a single qudit Lindbladian with quadratic non-linearity. We describe
three smoking guns for non-linear evolutions: Power law decay and dephasing
rates; Dephasing rates that take a continuous range of values depending on the
initial data and finally, anomalous flow of the Bloch ball towards a
hemisphere. | quant-ph |
An Introduction to Superconducting Qubits and Circuit Quantum
Electrodynamics: A subset of the concepts of circuit quantum electrodynamics are reviewed as a
reference to the Axion Dark Matter Experiment (ADMX) community as part of the
proceedings of the 2nd Workshop on Microwave Cavities and Detectors for Axion
Research. The classical Lagrangians and Hamiltonians for an LC circuit are
discussed along with black box circuit quantization methods for a weakly
anharmonic qubit coupled to a resonator or cavity. | quant-ph |
Quantum correlation in three-qubit Heisenberg model with
Dzyaloshinskii-Moriya interaction: We investigate the pairwise thermal quantum discord in a three-qubit XXZ
model with Dzyaloshinskii-Moriya (DM) interaction. We find that the DM
interaction can increase quantum discord to a fixed value in the anti-
ferromagnetic system, but decreases quantum discord to a minimum first, then
increases it to a fixed value in the ferromagnetic system. Abrupt change of
quantum discord is observed, which indicates the abrupt change of groundstate.
Dynamics of pairwise thermal quantum discord is also considered. We show that
thermal discord vanishes in asymptotic limit regardless of its initial values,
while thermal entanglement suddenly disappears at finite time. | quant-ph |
Resolving non-perturbative renormalization of a microwave-dressed weakly
anharmonic superconducting qubit: Microwave driving is a ubiquitous technique for superconducting qubits
(SCQs), but the dressed states description based on the conventionally used
perturbation theory cannot fully capture the dynamics in the strong driving
limit. Comprehensive studies beyond these approximations applicable to
transmon-based circuit quantum electrodynamics (QED) systems are unfortunately
rare as the relevant works have been mainly limited to single-mode or two-state
systems. In this work, we investigate a microwave-dressed transmon coupled to a
single quantized mode over a wide range of driving parameters. We reveal that
the interaction between the transmon and resonator as well as the properties of
each mode is significantly renormalized in the strong driving limit. Unlike
previous theoretical works, we establish a non-recursive, and non-Floquet
theory beyond the perturbative regimes, which excellently quantifies the
experiments. This work expands our fundamental understanding of dressed cavity
QED-like systems beyond the conventional approximations. Our work will also
contribute to fast quantum gate implementation, qubit parameter engineering,
and fundamental studies on driven nonlinear systems. | quant-ph |
Optical switching and inversionless amplification controlled by
state-dependent alignment of molecules: Switching anisotropic molecules from strongly-absorbing to
strongly-amplifying through a transparent state is shown to be possible by
application of dc or ac control electric fields without the requirement of the
population inversion. It is based on decoupling of the lower-level molecules
from the resonant light while the excited ones remain emitting due to their
state-dependent alignment. The amplification index may become dependent only on
a number of excited molecules and not on the population of the lower state. A
suitable class of molecules and applications in optoelectronics, fiberoptics
and nanophotonics are outlined. | quant-ph |
Modeling near ground-state cooling of two-dimensional ion crystals in a
Penning trap using electromagnetically induced transparency: Penning traps, with their ability to control planar crystals of tens to
hundreds of ions, are versatile quantum simulators. Thermal occupations of the
motional drumhead modes, transverse to the plane of the ion crystal, degrade
the quality of quantum simulations. Laser cooling using electromagnetically
induced transparency (EIT cooling) is attractive as an efficient way to quickly
initialize the drumhead modes to near ground-state occupations. We numerically
investigate the efficiency of EIT cooling of planar ion crystals in a Penning
trap, accounting for complications arising from the nature of the trap and from
the simultaneous cooling of multiple ions. We show that, in spite of
challenges, the large bandwidth of drumhead modes (hundreds of kilohertz) can
be rapidly cooled to near ground-state occupations within a few hundred
microseconds. Our predictions for the center-of-mass mode include a cooling
time constant of tens of microseconds and an enhancement of the cooling rate
with increasing number of ions. Successful experimental demonstrations of EIT
cooling in the NIST Penning trap [E. Jordan, K. A. Gilmore, A. Shankar, A.
Safavi-Naini, M. J. Holland, and J. J. Bollinger, "Near ground-state cooling of
two-dimensional trapped-ion crystals with more than 100 ions", (2018),
submitted.] validate our predictions. | quant-ph |
Dissipative many-body physics of cold Rydberg atoms: In the last twenty years, Rydberg atoms have become a versatile and much
studied system for implementing quantum many-body systems in the framework of
quantum computation and quantum simulation. However, even in the absence of
coherent evolution Rydberg systems exhibit interesting and non-trivial
many-body phenomena such as kinetic constraints and non-equilibrium phase
transitions that are relevant in a number of research fields. Here we review
our recent work on such systems, where dissipation leads to incoherent dynamics
and also to population decay. We show that those two effects, together with the
strong interactions between Rydberg atoms, give rise to a number of intriguing
phenomena that make cold Rydberg atoms an attractive test-bed for classical
many-body processes and quantum generalizations thereof. | quant-ph |
Resource Reduction in Multiplexed High-Dimensional Quantum Reed-Solomon
Codes: Quantum communication technologies will play an important role in quantum
information processing in the near future as we network devices together.
However, their implementation is still a challenging task due to both loss and
gate errors. Quantum error correction codes are one important technique to
address this issue. In particular, the Quantum Reed-Solomon codes are known to
be quite efficient for quantum communication tasks. The high degree of physical
resources required, however, makes such a code difficult to use in practice. A
recent technique called quantum multiplexing has been shown to reduce resources
by using multiple degrees of freedom of a photon. In this work, we propose a
method to decompose multi-controlled gates using fewer $\rm{CX}$ gates via this
quantum multiplexing technique. We show that our method can significantly
reduce the required number of $\rm{CX}$ gates needed in the encoding circuits
for the quantum Reed-Solomon code. Our approach is also applicable to many
other quantum error correction codes and quantum algorithms, including Grovers
and quantum walks. | quant-ph |
Supermeasured: Violating Bell-Statistical Independence without violating
physical statistical independence: Bell's theorem is often said to imply that quantum mechanics violates local
causality, and that local causality cannot be restored with a hidden-variables
theory. This however is only correct if the hidden-variables theory fulfils an
assumption called Statistical Independence. Violations of Statistical
Independence are commonly interpreted as correlations between the measurement
settings and the hidden variables (which determine the measurement outcomes).
Such correlations have been discarded as ``fine-tuning'' or a ``conspiracy''.
We here point out that the common interpretation is at best physically
ambiguous and at worst incorrect. The problem with the common interpretation is
that Statistical Independence might be violated because of a non-trivial
measure in state space, a possibility we propose to call ``supermeasured''. We
use Invariant Set Theory as an example of a supermeasured theory that violates
the Statistical Independence assumption in Bell's theorem without requiring
correlations between hidden variables and measurement settings (physical
statistical independence). | quant-ph |
A New Strategy of Quantum-State Estimation for Achieving the Cramer-Rao
Bound: We experimentally analyzed the statistical errors in quantum-state estimation
and examined whether their lower bound, which is derived from the Cramer-Rao
inequality, can be truly attained or not. In the experiments, polarization
states of bi-photons produced via spontaneous parametric down-conversion were
estimated employing tomographic measurements. Using a new estimation strategy
based on Akaike's information criterion, we demonstrated that the errors
actually approach the lower bound, while they fail to approach it using the
conventional estimation strategy. | quant-ph |
Analysis of the SGA method for obtaining energy spectra: We analyze and clarify how the SGA (spectrum generating algebra) method has
been applied to different potentials. We emphasize that each energy level
$E_\nu$ obtained originally by Morse belongs to a {\em different} ${\mathfrak
{so}}(2,1)$ multiplet. The corresponding wavefunctions $\Psi_\nu$ are
eigenfuntions of the compact generators $J^\nu_0$ with the same eigenvalue
$k_0$, but with different eigenvalues $q_\nu$ of the Casimir operators $Q$. We
derive a general expression for all effective potentials which have
$\Psi_{\lambda_\nu,\nu+m}(r) \propto (J_+^\nu)^m ~\Psi_{\lambda_\nu,\nu}(r)$ as
eigenfunctions, without using super-symmetry formalism. The different actions
of SGA is further illustrated by two diagrams. | quant-ph |
Accurate and Efficient Quantum Computations of Molecular Properties
Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against
Experimental Data: Although quantum computation (QC) is regarded as a promising numerical method
for computational quantum chemistry, current applications of quantum-chemistry
calculations on quantum computers are limited to small molecules. This
limitation can be ascribed to technical problems in building and manipulating
more qubits and the associated complicated operations of quantum gates in a
quantum circuit when the size of the molecular system becomes large. As a
result, reducing the number of required qubits is necessary to make QC
practical. Currently, the minimal STO-3G basis set is commonly used in
benchmark studies because it requires the minimum number of spin orbitals.
Nonetheless, the accuracy of using STO-3G is generally low and thus cannot
provide useful predictions. We propose to adopt Daubechies wavelet functions as
an accurate and efficient method for QCs of molecular electronic properties. We
demonstrate that a minimal basis set constructed from Daubechies wavelet basis
can yield accurate results through a better description of the molecular
Hamiltonian, while keeping the number of spin orbitals minimal. With the
improved Hamiltonian through Daubechies wavelets, we calculate vibrational
frequencies for H$_2$ and LiH using quantum-computing algorithm to show that
the results are in excellent agreement with experimental data. As a result, we
achieve quantum calculations in which accuracy is comparable with that of the
full configuration interaction calculation using the cc-pVDZ basis set, whereas
the computational cost is the same as that of a STO-3G calculation. Thus, our
work provides a more efficient and accurate representation of the molecular
Hamiltonian for efficient QCs of molecular systems, and for the first time
demonstrates that predictions in agreement with experimental measurements are
possible to be achieved with quantum resources available in near-term quantum
computers. | quant-ph |
Quantum correlations which imply causation: In ordinary, non-relativistic, quantum physics, time enters only as a
parameter and not as an observable: a state of a physical system is specified
at a given time and then evolved according to the prescribed dynamics. While
the state can, and usually does, extend across all space, it is only defined at
one instant of time, in conflict with special relativity where space and time
are treated on an equal footing. Here we ask what would happen if we defined
the notion of the quantum density matrix for multiple spatial and temporal
measurements. We introduce the concept of a pseudo-density matrix which treats
space and time indiscriminately. This matrix in general fails to be positive
for timelike separated measurements, motivating us to define a measure of
causality that discriminates between spacelike and timelike correlations.
Important properties of this measure, such as monotonicity under local
operations, are proved. Two qubit NMR experiments are presented that illustrate
how a temporal pseudo-density matrix approaches a genuinely allowed density
matrix as the amount of decoherence is increased between two consecutive
measurements. | quant-ph |
Driving Atoms Into Decoherence-Free States: We describe the decoherence-free subspace of N atoms in a cavity, in which
decoherence due to the leakage of photons through the cavity mirrors is
suppressed. We show how the states of the subspace can be entangled with the
help of weak laser pulses, using the high decay rate of the cavity field and
strong coupling between the atoms and the resonator mode. The atoms remain
decoherence-free with a probability which can, in principle, be arbitrarily
close to unity. | quant-ph |
Decomposition of bipartite and multipartite unitary gates into the
product of controlled unitary gates: We show that any unitary operator on the $d_A\times d_B$ system ($d_A\ge 2$)
can be decomposed into the product of at most $4d_A-5$ controlled unitary
operators. The number can be reduced to $2d_A-1$ when $d_A$ is a power of two.
We also prove that three controlled unitaries can implement a bipartite complex
permutation operator, and discuss the connection to an analogous result on
classical reversible circuits. We further show that any $n$-partite unitary on
the space $\mathbb{C}^{d_1}\otimes...\otimes\mathbb{C}^{d_n}$ is the product of
at most $[2\prod^{n-1}_{j=1}(2d_j-2)-1]$ controlled unitary gates, each of
which is controlled from $n-1$ systems. The number can be further reduced for
$n=4$. We also decompose any bipartite unitary into the product of a simple
type of bipartite gates and some local unitaries. We derive
dimension-independent upper bounds for the CNOT-gate cost or entanglement cost
of bipartite permutation unitaries (with the help of ancillas of fixed size) as
functions of the Schmidt rank of the unitary. It is shown that such costs under
a simple protocol are related to the log-rank conjecture in communication
complexity theory via the link of nonnegative rank. | quant-ph |
Bell's inequality violation for entangled generalized Bernoulli states
in two spatially separate cavities: We consider the entanglement of orthogonal generalized Bernoulli states in
two separate single-mode high-$Q$ cavities. The expectation values and the
correlations of the electric field in the cavities are obtained. We then
define, in each cavity, a dichotomic operator expressible in terms of the field
states which can be, in principle, experimentally measured by a probe atom that
``reads'' the field. Using the quantum correlations of couples of these
operators, we construct a Bell's inequality which is shown to be violated for a
wide range of the degree of entanglement and which can be tested in a simple
way. Thus the cavity fields directly show quantum non-local properties. A
scheme is also sketched to generate entangled orthogonal generalized Bernoulli
states in the two separate cavities. | quant-ph |
Indistinguishable Encoding for Bidirectional Quantum Key Distribution:
Theory to Experiment: We present for the first time, a bidirectional Quantum Key Distribution
protocol with minimal encoding operations derived from the use of two
`nonorthogonal' unitary transformations selected from two mutually unbiased
unitary bases; which are indistinguishable in principle for a single use. Along
with its decoding procedure, it is a stark contrast to its `orthogonal
encoding' predecessors. Defining a more relevant notion of security threshold
for such protocols, the current protocol outperforms its predecessor in terms
of security as the maximal amount of information an eavesdropper can glean is
essentially limited by the indistinguishability of the transformations. We
further propose adaptations for a practical scenario and report on a proof of
concept experimental scheme based on polarised photons from an attenuated
pulsed laser for qubits, demonstrating the feasibility of such a protocol. | quant-ph |
Control of spontaneous emission of qubits from weak to strong coupling: Photon emission and absorption by an individual qubit are essential elements
for the quantum manipulation of light. Here we demonstrate the controllability
of spontaneous emission of a qubit in various electromagnetic environments. The
parameter regimes that allow for exible control of the qubit emission routes
are comprehensively discussed. By properly tuning the system couplings and
decay rates, the spontaneous emission rate of the qubit can undergo Purcell
enhancement and inhibition. Particularly, when the cavity is prepared in the
excited state, the spontaneous emission rate of the qubit can be significantly
suppressed. We also demonstrate a spectral filter effect which can be realised
by controlling the steady-state emission spectra of qubits. | quant-ph |
Adiabatic Product Expansion: The time-evolution operator for an explicitly time-dependent Hamiltonian is
expressed as the product of a sequence of unitary operators. These are obtained
by successive time-dependent unitary transformations of the Hilbert space
followed by the adiabatic approximation at each step. The resulting adiabatic
product expansion yields a generalization of the quantum adiabatic
approximation. Furthermore, it leads to an infinite class of exactly solvable
models. | quant-ph |
Spin-echo entanglement protection from random telegraph noise: We analyze local spin-echo procedures to protect entanglement between two
non-interacting qubits, each subject to pure-dephasing random telegraph noise.
For superconducting qubits this simple model captures characteristic features
of the effect of bistable impurities coupled to the device. An analytic
expression for the entanglement dynamics is reported. Peculiar features related
to the non-Gaussian nature of the noise already observed in the single qubit
dynamics also occur in the entanglement dynamics for proper values of the ratio
$g=v/\gamma$, between the qubit-impurity coupling strength and the switching
rate of the random telegraph process, and of the separation between the pulses
$\Delta t$. We find that the echo procedure may delay the disappearance of
entanglement, cancel the dynamical structure of entanglement revivals and dark
periods, and induce peculiar plateau-like behaviors of the concurrence. | quant-ph |
Effect of Decoherence for Gate Operations on a Superconducting Bosonic
Qubit: High-quality-factor 3D cavities in superconducting circuits are ideal
candidates for bosonic logical qubits as their fidelity is limited only by the
low photon loss rate. However, the transmon qubits that are used to manipulate
bosonic qubits result in the emergence of additional relaxation and dephasing
channels. In this work, a numerical study is performed to elucidate the effect
of the various loss channels on the performance of logical gates on a bosonic
qubit. A gate error model is developed that encapsulates the loss mechanisms
for arbitrary gate operations and predicts experimentally achievable gate
errors for bosonic qubits. The insights gleaned from this study into loss
mechanisms suggest more efficient optimization algorithms that could reduce
gate errors on bosonic qubits. | quant-ph |
Sub-Attosecond Metrology via X-Ray Hong-Ou-Mandel Effect: We show that sub-attosecond delays and sub-Angstrom optical path differences
can be measured by using Hong-Ou-Mandel interference measurements with x-rays.
We propose to use a system comprising a source based on spontaneous parametric
down-conversion for the generation of broadband x-ray photon pairs and a
multilayer-based interferometer. The correlation time of the photon pairs and
the Hong-Ou-Mandel dip are shorter than 1 attosecond, hence the precision of
the measurements is expected to be better than 0.1 attosecond. We anticipate
that the scheme we describe in this work will lead to the development of
various techniques of quantum measurements with ultra-high precision at x-ray
wavelengths. | quant-ph |
Quantum control of "quantum triple collisions" in a maximally symmetric
three-body Coulomb problem: In Coulomb 3-body problems, configurations of close proximity of the
particles are classically unstable. In confined systems they might however
exist as excited quantum states. Quantum control of such states by time
changing electromagnetic fields is discussed. | quant-ph |
Stabilization of nonclassical states of one- and two-mode radiation
fields by reservoir engineering: We analyze a quantum reservoir engineering method, originally introduced by
[Sarlette et al. in Phys. Rev. Lett. 107, 010402 (2011) -- arXiv 1011.5057],
for the stabilization of non-classical field states in high quality cavities.
We generalize the method to the protection of mesoscopic entangled field states
shared by two non-degenerate field modes. The reservoir is made up of a stream
of atoms undergoing successive composite interactions with the cavity, each
combining resonant with non-resonant parts. We get a detailed insight into the
competition between the engineered reservoir and decoherence. We show that the
operation is quite insensitive to experimental imperfections and that it could
thus be implemented in the near future, either in the context of microwave
Cavity Quantum Electrodynamics or in that of circuit-QED. | quant-ph |
Magnetic-field-learning using a single electronic spin in diamond with
one-photon-readout at room temperature: Nitrogen-vacancy (NV) centres in diamond are appealing nano-scale quantum
sensors for temperature, strain, electric fields and, most notably, for
magnetic fields. However, the cryogenic temperatures required for low-noise
single-shot readout that have enabled the most sensitive NV-magnetometry
reported to date, are impractical for key applications, e.g. biological
sensing. Overcoming the noisy readout at room-temperature has until now
demanded repeated collection of fluorescent photons, which increases the
time-cost of the procedure thus reducing its sensitivity. Here we show how
machine learning can process the noisy readout of a single NV centre at
room-temperature, requiring on average only one photon per algorithm step, to
sense magnetic field strength with a precision comparable to those reported for
cryogenic experiments. Analysing large data sets from NV centres in bulk
diamond, we report absolute sensitivities of $60$ nT s$^{1/2}$ including
initialisation, readout, and computational overheads. We show that dephasing
times can be simultaneously estimated, and that time-dependent fields can be
dynamically tracked at room temperature. Our results dramatically increase the
practicality of early-term single spin sensors. | quant-ph |
Temperature-Controlled Entangled-Photon Absorption Spectroscopy: Entangled two-photon absorption spectroscopy (TPA) has been widely recognized
as a powerful tool for revealing relevant information about the structure of
complex molecular systems. However, to date, the experimental implementation of
this technique has remained elusive, mainly because of two major difficulties.
First, the need to perform multiple experiments with two-photon states bearing
different temporal correlations, which translates in the necessity to have at
the experimenter's disposal tens, if not hundreds, of sources of entangled
photons. Second, the need to have \emph{a priori} knowledge of the absorbing
medium's lowest-lying intermediate energy level. In this work, we put forward a
simple experimental scheme that successfully overcomes these two limitations.
By making use of a temperature-controlled entangled-photon source, which allows
the tuning of the central frequencies of the absorbed photons, we show that the
TPA signal, measured as a function of the temperature of the nonlinear crystal
that generates the paired photons, and a controllable delay between them,
carries all information about the electronic level structure of the absorbing
medium, which can be revealed by a simple Fourier transformation. | quant-ph |
Uncertainty relation between detection probability and energy
fluctuations: A classical random walker starting on a node of a finite graph will always
reach any other node since the search is ergodic, namely it is fully exploring
space, hence the arrival probability is unity. For quantum walks, destructive
interference may induce effectively non-ergodic features in such search
processes. Under repeated projective local measurements, made on a target
state, the final detection of the system is not guaranteed since the Hilbert
space is split into a bright subspace and an orthogonal dark one. Using this we
find an uncertainty relation for the deviations of the detection probability
from its classical counterpart, in terms of the energy fluctuations. | quant-ph |
Single-atom single-photon coupling facilitated by atomic-ensemble
dark-state mechanisms: We propose to couple single atomic qubits to photons incident on a cavity
containing an atomic ensemble of a different species that mediates the coupling
via Rydberg interactions. Subject to a classical field and the cavity field,
the ensemble forms a collective dark state which is resonant with the input
photon, while excitation of a qubit atom leads to a secondary "dark" state that
splits the cavity resonance. The two different dark state mechanisms yield zero
and $\pi$ reflection phase shifts and can be used to implement quantum gates
between atomic and optical qubits. | quant-ph |
Remote two-qubit state creation and its robustness: We consider the problem of remote two-qubit state creation using the
two-qubit excitation pure initial state of the sender. The communication line
is based on the optimized boundary controlled chain with two pairs of properly
adjusted coupling constants. The creation of the two-qubit Werner state is
considered as an example. We also study the effects of imperfections of the
chain on the state-creation. | quant-ph |
How Much Structure Is Needed for Huge Quantum Speedups?: I survey, for a general scientific audience, three decades of research into
which sorts of problems admit exponential speedups via quantum computers --
from the classics (like the algorithms of Simon and Shor), to the breakthrough
of Yamakawa and Zhandry from April 2022. I discuss both the quantum circuit
model, which is what we ultimately care about in practice but where our
knowledge is radically incomplete, and the so-called oracle or black-box or
query complexity model, where we've managed to achieve a much more thorough
understanding that then informs our conjectures about the circuit model. I
discuss the strengths and weaknesses of switching attention to sampling tasks,
as was done in the recent quantum supremacy experiments. I make some skeptical
remarks about widely-repeated claims of exponential quantum speedups for
practical machine learning and optimization problems. Through many examples, I
try to convey the "law of conservation of weirdness," according to which every
problem admitting an exponential quantum speedup must have some unusual
property to allow the amplitude to be concentrated on the unknown right
answer(s). | quant-ph |
Cannikin's Law in Tensor Modeling: A Rank Study for Entanglement and
Separability in Tensor Complexity and Model Capacity: This study clarifies the proper criteria to assess the modeling capacity of a
general tensor model. The work analyze the problem based on the study of tensor
ranks, which is not a well-defined quantity for higher order tensors. To
process, the author introduces the separability issue to discuss the Cannikin's
law of tensor modeling. Interestingly, a connection between entanglement
studied in information theory and tensor analysis is established, shedding new
light on the theoretical understanding for modeling capacity problems. | quant-ph |
Non-Markovian waiting time distribution: Simulation methods based on stochastic realizations of state vector
evolutions are commonly used tools to solve open quantum system dynamics, both
in the Markovian and non-Markovian regime. Here, we address the question of
waiting time distribution (WTD) of quantum jumps for non-Markovian systems. We
generalize Markovian quantum trajectory methods in the sense of deriving an
exact analytical WTD for non-Markovian quantum dynamics and show explicitly how
to construct this distribution for certain commonly used quantum optical
systems. | quant-ph |
Generation of NPT Entanglement from Nonclassical Photon Statistics: With a product state of the form $\rho_{in} = \rho_a\otimes|0>_b_b< 0|$ as
input, the output two-mode state $\rho_{{\rm out}}$, of the beam splitter is
shown to be NPT whenever the photon number distribution (PND) statistics
$\{p(n_a) \}$ associated with the possibly mixed state $\rho_a$ of the a_mode
is antibunched or otherwise nonclassical, i.e., if $\{p(n_a)\}$ fails to
respect any one of an infinite of classicality conditions. | quant-ph |
Nonlocality at detection and conservation of energy. Was Einstein
looking for an "epistemic" interpretation, a "superdeterministic" one, or
both?: In the Solvay conference (1927) Einstein argued against the quantum nonlocal
decision at detection on the basis of a simple single-particle experiment, but
thereafter he withdrew towards the more complicated 2-particle EPR argument. It
has been claimed that Einstein was seeking for an "epistemic interpretation".
In the light of a recent experiment I argue that Einstein missed an important
point: One cannot have conservation of energy without nonlocality at detection.
This experiment refutes also straightforwardly "epistemic" and "ontic"
alternatives to quantum theory, and shows that Einstein's "epistemicism"
entails "superdeterminism". | quant-ph |
Low-depth Gaussian State Energy Estimation: Recent progress in quantum computing is paving the way for the realization of
early fault-tolerant quantum computers. To maximize the utility of these
devices, it is important to develop quantum algorithms that match their
capabilities and limitations. Motivated by this, recent work has developed
low-depth quantum algorithms for ground state energy estimation (GSEE), an
important subroutine in quantum chemistry and materials. We detail a new GSEE
algorithm which, like recent work, uses a number of operations scaling as
$O(1/\Delta)$ as opposed to the typical $O(1/\epsilon)$, at the cost of an
increase in the number of circuit repetitions from $O(1)$ to $O(1/\epsilon^2)$.
The relevant features of this algorithm come about from using a Gaussian
window, which exponentially reduces contamination from excited states over the
simplest GSEE algorithm based on the Quantum Fourier Transform (QFT). We adapt
this algorithm to interpolate between the low-depth and full-depth regime by
replacing $\Delta$ with anything between $\Delta$ and $\epsilon$. At the cost
of increasing the number of ancilla qubits from $1$ to $O(\log\Delta)$, our
method reduces the upper bound on the number of circuit repetitions by a factor
of four compared to previous methods. | quant-ph |
Quantum Blackjack or Can MIT Bring Down the House Again?: We examine the advantages that quantum strategies afford in
communication-limited games. Inspired by the card game blackjack, we focus on
cooperative, two-party sequential games in which a single classical bit of
communication is allowed from the player who moves first to the player who
moves second. Within this setting, we explore the usage of quantum entanglement
between the players and find analytic and numerical conditions for quantum
advantage over classical strategies. Using these conditions, we study a family
of blackjack-type games with varying numbers of card types, and find a range of
parameters where quantum advantage is achieved. Furthermore, we give an
explicit quantum circuit for the strategy achieving quantum advantage. | quant-ph |
Entanglement evolution in a cascaded system with losses: The dynamics of a cascaded system that consists of two atom-cavity subsystems
is studied by using the quantum trajectory method. Unwanted losses are
included, such as photon absorption and scattering by the cavity mirrors and
spontaneous emission of the atoms. Considering an initially excited two-level
atom in the source subsystem, analytical solutions are obtained. The
entanglement evolution is studied for the two atoms and for the two intracavity
fields. | quant-ph |
Routing quantum information in spin chains: Two different models for performing efficiently routing of a quantum state
are presented. Both cases involve an XX spin chain working as data bus and
additional spins that play the role of sender and receivers, one of which is
selected to be the target of the quantum state transmission protocol via a
coherent quantum coupling mechanism making use of local/global magnetic fields.
Quantum routing is achieved, in the first of the models considered, by weakly
coupling the sender and the receiver to the data bus. In the second model,
strong magnetic fields acting on additional spins located between the
sender/receiver and the data bus allow us to perform high fidelity routing. | quant-ph |
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic
oscillator: The generalized Swanson Hamiltonian $H_{GS} = w (\tilde{a}\tilde{a}^\dag+
1/2) + \alpha \tilde{a}^2 + \beta \tilde{a}^{\dag^2}$ with $\tilde{a} =
A(x)d/dx + B(x)$, can be transformed into an equivalent Hermitian Hamiltonian
with the help of a similarity transformation. It is shown that the equivalent
Hermitian Hamiltonian can be further transformed into the harmonic oscillator
Hamiltonian so long as $[\tilde{a},\tilde{a}^\dag]=$ constant. However, the
main objective of this paper is to show that though the commutator of
$\tilde{a}$ and $\tilde{a}^\dag$ is constant, the generalized Swanson
Hamiltonian is not necessarily isospectral to the harmonic oscillator. Reason
for this anomaly is discussed in the frame work of position dependent mass
models by choosing $A(x)$ as the inverse square root of the mass function. | quant-ph |
Efficient Coherent Control by Optimized Sequences of Pulses of Finite
Duration: Reliable long-time storage of arbitrary quantum states is a key element for
quantum information processing. In order to dynamically decouple a spin or
quantum bit from a dephasing environment, we introduce an optimized sequence of
$N$ control pulses of finite durations $\tau\pp$ and finite amplitudes. The
properties of this sequence of length $T$ stem from a mathematically rigorous
derivation. Corrections occur only in order $T^{N+1}$ and $\tau\pp^3$ without
mixed terms such as $T^N\tau\pp$ or $T^N\tau\pp^2$. Based on existing
experiments, a concrete setup for the verification of the properties of the
advocated realistic sequence is proposed. | quant-ph |
Entanglement of distant optomechanical systems: We theoretically investigate the possibility to generate non-classical states
of optical and mechanical modes of optical cavities, distant from each other. A
setup comprised of two identical cavities, each with one fixed and one movable
mirror and coupled by an optical fiber, is studied in detail. We show that with
such a setup there is potential to generate entanglement between the distant
cavities, involving both optical and mechanical modes. The scheme is robust
with respect to dissipation, and nonlocal correlations are found to exist in
the steady state at finite temperatures. | quant-ph |
Pump-efficient Josephson parametric amplifiers with high saturation
power: Circuit QED based quantum information processing relies on low noise
amplification for signal readout. In the realm of microwave superconducting
circuits, this amplification is often achieved via Josephson parametric
amplifiers (JPA). In the past, these amplifiers exhibited low power added
efficiency (PAE), which is roughly the fraction of pump power that is converted
to output signal power. This is increasingly relevant because recent attempts
to build high saturation power amplifiers achieve this at the cost of very low
PAE, which in turn puts a high heat load on the cryostat and limits the number
of these devices that a dilution refrigerator can host. Here, we numerically
investigate upper bounds on PAE. We focus on a class of parametric amplifiers
that consists of a capacitor shunted by a nonlinear inductive block. We first
set a benchmark for this class of amplifiers by considering nonlinear blocks
described by an arbitrary polynomial current-phase relation. Next, we propose
two circuit implementations of the nonlinear block. Finally, we investigate
chaining polynomial amplifiers. We find that while amplifiers with higher gain
have a lower PAE, regardless of the gain there is considerable room to improve
as compared to state of the art devices. For example, for a phase-sensitive
amplifier with a power gain of 20 dB, the PAE is ~0.1% for typical JPAs, 5.9%
for our simpler circuit JPAs, 34% for our more complex circuit JPAs, 48% for
our arbitrary polynomial amplifiers, and at least 95% for our chained
amplifiers. | quant-ph |
Pre-Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body
systems: The sixteen-component, no-pair Dirac--Coulomb--Breit equation, derived from
the Bethe--Salpeter equation, is solved in a variational procedure using
Gaussian-type basis functions for the example of positronium, muonium, hydrogen
atom, and muonic hydrogen. The $\alpha$ fine-structure-constant dependence of
the variational energies, through fitting a function of $\alpha^n$ and
$\alpha^n\text{ln}\alpha$ terms, shows excellent agreement with the relevant
energy expressions of the (perturbative) non-relativistic QED framework, and
thereby, establishes a solid reference for the development of a computational
relativistic QED approach. | quant-ph |
A Non-Local Reality: Is there a Phase Uncertainty in Quantum Mechanics?: A century after the advent of Quantum Mechanics and General Relativity, both
theories enjoy incredible empirical success, constituting the cornerstones of
modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far
intractable, conflicts. Motivations for violations of the notion of
relativistic locality include the Bell's inequalities for hidden variable
theories, the cosmological horizon problem, and Lorentz-violating approaches to
quantum geometrodynamics, such as Horava-Lifshitz gravity. Here, we explore a
recent proposal for a "real ensemble" non-local description of quantum
mechanics, in which "particles" can copy each others' observable values AND
phases, independent of their spatial separation. We first specify the exact
theory, ensuring that it is consistent and has (ordinary) quantum mechanics as
a fixed point, where all particles with the same values for a given observable
have the same phases. We then study the stability of this fixed point
numerically, and analytically, for simple models. We provide evidence that most
systems (in our study) are locally stable to small deviations from quantum
mechanics, and furthermore, the phase variance per value of the observable, as
well as systematic deviations from quantum mechanics, decay as $\sim$
(Energy$\times$Time)$^{-2n}$, where $n \geq 1$. Interestingly, this convergence
is controlled by the absolute value of energy (and not energy difference),
suggesting a possible connection to gravitational physics. Finally, we discuss
different issues related to this theory, as well as potential novel
applications for the spectrum of primordial cosmological perturbations and the
cosmological constant problem. | quant-ph |
Activated and non activated dephasing demonstrated in NV center dynamics: We analyze different decoherence processes in a system coupled to a bath.
Apart from the well known standard dephasing mechanism which is temperature
dependent an alternative mechanism is presented, the spin-swap dephasing which
does not need initial bath activation and is temperature independent. We show
that for dipolar interaction the separation of time scales between system and
bath can not produce pure dephasing, the process being accompained by
dissipation. Activated and non activated dephasing processes are demonstrated
in a diamond nitrogen-vacancy (NV) center. | quant-ph |
Topological lattices realized in superconducting circuit optomechanics: Cavity optomechanics enables controlling mechanical motion via radiation
pressure interaction, and has contributed to the quantum control of engineered
mechanical systems ranging from kg scale LIGO mirrors to nano-mechanical
systems, enabling ground-state preparation, entanglement, squeezing of
mechanical objects, position measurements at the standard quantum limit and
quantum transduction. Yet, nearly all prior schemes have employed single- or
few-mode optomechanical systems. In contrast, novel dynamics and applications
are expected when utilizing optomechanical lattices, which enable to synthesize
non-trivial band structures, and have been actively studied in the field of
circuit QED. Superconducting microwave optomechanical circuits are a promising
platform to implement such lattices, but have been compounded by strict scaling
limitations. Here, we overcome this challenge and demonstrate topological
microwave modes in 1D circuit optomechanical chains realizing the
Su-Schrieffer-Heeger (SSH) model. Furthermore, we realize the strained graphene
model in a 2D optomechanical honeycomb lattice. Exploiting the embedded
optomechanical interaction, we show that it is possible to directly measure the
mode functions of the hybridized modes without using any local probe. This
enables us to reconstruct the full underlying lattice Hamiltonian and directly
measure the existing residual disorder. Such optomechanical lattices,
accompanied by the measurement techniques introduced, offers an avenue to
explore collective, quantum many-body, and quench dynamics, topological
properties and more broadly, emergent nonlinear dynamics in complex
optomechanical systems with a large number of degrees of freedoms.
(Keywords: Quantum Optomechanics, Superconducting Circuit Electromecahnics) | quant-ph |
Internal entanglement and external correlations of any form limit each
other: We show a relation between entanglement and correlations of any form. The
internal entanglement of a bipartite system, and its correlations with another
system, limit each other. A measure of correlations, of any nature, cannot
increase under local operations. Examples are the entanglement monotones, the
mutual information, that quantifies total correlations, and the
Henderson-Vedral measure of classical correlations. External correlations,
evaluated by such a measure, set a tight upper bound on the internal
entanglement that decreases as they increase, and so does quantum discord. | quant-ph |
Classical and quantum chaos in a three-mode bosonic system: We study the dynamics of a three-mode bosonic system with mode-changing
interactions. For large mode occupations the short-time dynamics is well
described by classical mean-field equations allowing us to study chaotic
dynamics in the classical system and its signatures in the corresponding
quantum dynamics. By introducing a symmetry-breaking term we tune the classical
dynamics from integrable to strongly chaotic which we demonstrate by
calculating Poincar\'e sections and Lyapunov exponents. The corresponding
quantum system features level statistics that change from Poissonian in the
integrable to Wigner-Dyson in the chaotic case. We investigate the behavior of
out-of-time-ordered correlators (OTOCs), specifically the squared commutator,
for initial states located in regular and chaotic regions of the classical
mixed phase space and find marked differences between the two cases. The
short-time behavior is well captured by semi-classical truncated Wigner
simulations directly relating these features to properties of the underlying
classical mean field dynamics. We discuss a possible experimental realization
of this model system in a Bose-Einstein condensate of rubidium atoms which
allows reversing the sign of the Hamiltonian required for measuring OTOCs
experimentally. | quant-ph |
Theory of atomic diffraction from evanescent waves: We review recent theoretical models and experiments dealing with the
diffraction of neutral atoms from a reflection grating, formed by a standing
evanescent wave. We analyze diffraction mechanisms proposed for normal and
grazing incidence, point out their scopes and confront the theory with
experiment. | quant-ph |
Generalized distillability conjecture and generalizations of
Cauchy-Bunyakovsky-Schwarz inequality and Lagrange identity: Let rho_k, k=1,2,...,m, be the critical Werner state in a bipartite d_k by
d_k quantum system, i.e., the one that separates the 1-distillable Werner
states from those that are 1-indistillable. We propose a new conjecture (GDC)
asserting that the tensor product of rho_k is 1-indistillable. This is much
stronger than the familiar conjecture saying that a single critical Werner
state is indistillable. We prove that GDC is true for arbitrary m provided that
d_k is bigger than 2 for at most one index k. We reformulate GDC as an
intriguing inequality for four arbitrary complex hypermatrices of type d_1 x
... x d_m. This hypermatrix inequality is just the special case n=2 of a more
general conjecture (CBS conjecture) for 2n arbitrary complex hypermatrices of
the same type. Surprisingly, the case n=1 turns out to be quite interesting as
it provides hypermatrix generalization of the classical Lagrange identity. We
also formulate the integral version of the CBS conjecture and derive the
integral version of the hypermatrix Lagrange identity. | quant-ph |
Nonadditive entropy for random quantum spin-S chains: We investigate the scaling of Tsallis entropy in disordered quantum spin-S
chains. We show that an extensive scaling occurs for specific values of the
entropic index. Those values depend only on the magnitude S of the spins, being
directly related with the effective central charge associated with the model. | quant-ph |
Boltzmann machines as thermal models for quantum systems: We successfully model the behavior of two-spin systems using neural networks
known as conditional Restricted Boltzmann Machines (cRBMs) which encode
physical information in the properties of a thermal ensemble akin to an Ising
model. The result gives local "hidden" variable models for product states and
entangled states, including the singlet state used in the EPR-Bohm experiment.
Bell's theorem is circumvented because the state of the system is dependent not
only on the preparation but also on the measurement setup (the detector
settings). Though at first glance counterintuitive, the apparent
"retrocausality" in these models has a historical precedent in the absorber
theory of Wheeler and Feynman and an intuitive analog in the simple AC circuit
of an electric guitar. | quant-ph |
Bohmian transmission and reflection dwell times without trajectory
sampling: Within the framework of Bohmian mechanics dwell times find a straightforward
formulation. The computation of associated probabilities and distributions
however needs the explicit knowledge of a relevant sample of trajectories and
therefore implies formidable numerical effort. Here a trajectory free
formulation for the average transmission and reflection dwell times within
static spatial intervals [a,b] is given for one-dimensional scattering
problems. This formulation reduces the computation time to less than 5% of the
computation time by means of trajectory sampling. | quant-ph |
Subsets and Splits