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Superhyperfine induced photon-echo collapse of erbium in Y$_2$SiO$_5$: We investigate the decoherence of Er$^{3+}$ in Y$_2$SiO$_5$ at low magnetic
fields using the photon-echo technique. We reproduce accurately a variety of
the decay curves with a unique coherence time by considering the so-called
superhyperfine modulation induced by a large number of neighbouring spins.
There is no need to invoke any characteristic time of the spin fluctuations to
reproduce very different decay curves. The number of involved nuclei increases
when the magnetic is lowered. The experiment is compared with a model
associating 100 surrounding ions with their exact positions in the crystal
frame. We also derive an approximate spherical model (angular averaging) to
interpret the main feature the observed decay curves close to zero-field.
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quant-ph
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Hamiltonian point of view of quantum perturbation theory: We explore the relation of Van Vleck-Primas perturbation theory of quantum
mechanics with the Lie-series based perturbation theory of Hamiltonian systems
in classical mechanics. In contrast to previous works on the relation of
quantum and classical perturbation theories, our approach is not based on the
conceptual similarities between the two methods. Instead, we show that for
quantum systems with a finite-dimensional Hilbert space, the Van Vleck-Primas
procedure can be recast exactly into a classical perturbation problem.
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quant-ph
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Analysis of Coined Quantum Walks with Renormalization: We introduce a new framework to analyze quantum algorithms with the
renormalization group (RG). To this end, we present a detailed analysis of the
real-space RG for discrete-time quantum walks on fractal networks and show how
deep insights into the analytic structure as well as generic results about the
long-time behavior can be extracted. The RG-flow for such a walk on a dual
Sierpinski gasket and a Migdal-Kadanoff hierarchical network is obtained
explicitly from elementary algebraic manipulations, after transforming the
unitary evolution equation into Laplace space. Unlike for classical random
walks, we find that the long-time asymptotics for the quantum walk requires
consideration of a diverging number of Laplace-poles, which we demonstrate
exactly for the closed form solution available for the walk on a 1d-loop. In
particular, we calculate the probability of the walk to overlap with its
starting position, which oscillates with a period that scales as
$N^{d_{w}^{Q}/d_{f}}$ with system size $N$. While the largest Jacobian
eigenvalue $\lambda_{1}$ of the RG-flow merely reproduces the fractal
dimension, $d_{f}=\log_{2}\lambda_{1}$, the asymptotic analysis shows that the
second Jacobian eigenvalue $\lambda_{2}$ becomes essential to determine the
dimension of the quantum walk via
$d_{w}^{Q}=\log_{2}\sqrt{\lambda_{1}\lambda_{2}}$. We trace this fact to
delicate cancellations caused by unitarity. We obtain identical relations for
other networks, although the details of the RG-analysis may exhibit
surprisingly distinct features. Thus, our conclusions -- which trivially
reproduce those for regular lattices with translational invariance with
$d_{f}=d$ and $d_{w}^{Q}=1$ -- appear to be quite general and likely apply to
networks beyond those studied here.
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quant-ph
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Construction of Energy Functions for Lattice Heteropolymer Models: A
Case Study in Constraint Satisfaction Programming and Adiabatic Quantum
Optimization: Optimization problems associated with the interaction of linked particles are
at the heart of polymer science, protein folding and other important problems
in the physical sciences. In this review we explain how to recast these
problems as constraint satisfaction problems such as linear programming,
maximum satisfiability, and pseudo-boolean optimization. By encoding problems
this way, one can leverage substantial insight and powerful solvers from the
computer science community which studies constraint programming for diverse
applications such as logistics, scheduling, artificial intelligence, and
circuit design. We demonstrate how to constrain and embed lattice heteropolymer
problems using several strategies. Each strikes a unique balance between number
of constraints, complexity of constraints, and number of variables. Finally, we
show how to reduce the locality of couplings in these energy functions so they
can be realized as Hamiltonians on existing quantum annealing machines. We
intend that this review be used as a case study for encoding related
combinatorial optimization problems in a form suitable for adiabatic quantum
optimization.
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quant-ph
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Localization and limit laws of a three-state alternate quantum walk on a
two-dimensional lattice: A two-dimensional discrete-time quantum walk (DTQW) can be realized by
alternating a two-state DTQW in one spatial dimension followed by an evolution
in the other dimension. This was shown to reproduce a probability distribution
for a certain configuration of a four-state DTQW on a two-dimensional lattice.
In this work we present a three-state alternate DTQW with a parameterized
coin-flip operator and show that it can produce localization that is also
observed for a certain other configuration of the four-state DTQW and
non-reproducible using the two-state alternate DTQW. We will present two limit
theorems for the three-state alternate DTQW. One of the limit theorems
describes a long-time limit of a return probability, and the other presents a
convergence in distribution for the position of the walker on a rescaled space
by time. We will also outline the relevance of these walks in physical systems.
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quant-ph
|
Entanglement of extremal density matrices of 2-qubit Hamiltonian with
Kramers degeneracy: We establish a novel procedure to analyze the entanglement properties of
extremal density matrices depending on the parameters of a finite dimensional
Hamiltonian. It was applied to a general 2-qubit Hamiltonian which could
exhibit Kramers degeneracy. This is done through the extremal density matrix
formalism, which allows to extend the conventional variational principle to
mixed states. By applying the positive partial transpose criterion in terms of
the Correlation and Schlienz-Mahler matrices on the extremal density matrices,
we demonstrate that it is possible to reach both pure and mixed entangled
states, changing properly the parameters of the Hamiltonian. For time-reversal
invariant Hamiltonians, the extremal pure states can be entangled or not and we
prove that they are not time-reversal invariants. For extremal mixed states we
have in general 5 possible cases: three of them are entangled and the other two
separable.
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quant-ph
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Particle pair creation by inflation of quantum vacuum fluctuations in an
ion trap: The creation of matter and structure in our universe is currently described
by an intricate interplay of quantum field theory and general relativity.
Signatures of this process during an early inflationary period can be observed,
while direct tests remain out of reach. Here, we study an experimental analog
of the process based on trapped atomic ions. We create pairs of phonons by
tearing apart quantum vacuum fluctuations. Thereby, we prepare ions in an
entangled state of motion. Controlling timescales and the coupling to
environments should permit optimizing efficiencies while keeping the effect
robust via established tools in quantum information processing (QIP). This
might also permit to cross-fertilize between concepts in cosmology and
applications of QIP, such as, quantum metrology, experimental quantum
simulations and quantum computing.
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quant-ph
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Meltdown in quantum computers needs not occur: Nuclear experiments show
a way out: We show that phase memory can be much longer than energy relaxation in
systems with exponentially large dimensions of Hilbert space; this finding is
documented by fifty years of nuclear experiments, though the information is
somewhat hidden. For quantum computers Hilbert spaces of dimension $2^{100}$ or
larger will be typical and therefore this effect may contribute significantly
to reduce the problems of scaling of quantum computers to a useful number of
qubits.
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quant-ph
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Phase space methods for Majorana fermions: Fermionic phase space representations are a promising method for studying
correlated fermion systems. The fermionic Q-function and P-function have been
defined using Gaussian operators of fermion annihilation and creation
operators. The resulting phase-space of covariance matrices belongs to the
symmetry class D, one of the non-standard symmetry classes. This was originally
proposed to study mesoscopic normal-metal-superconducting hybrid structures,
which is the type of structure that has led to recent experimental observations
of Majorana fermions. Under a unitary transformation, it is possible to express
these Gaussian operators using real anti-symmetric matrices and Majorana
operators, which are much simpler mathematical objects. We derive differential
identities involving Majorana fermion operators and an antisymmetric matrix
which are relevant to the derivation of the corresponding Fokker-Planck
equations on symmetric space. These enable stochastic simulations either in
real or imaginary time. This formalism has direct relevance to the study of
fermionic systems in which there are Majorana type excitations, and is an
alternative to using expansions involving conventional Fermi operators. The
approach is illustrated by showing how a linear coupled Hamiltonian as used to
study topological excitations can be transformed to Fokker-Planck and
stochastic equation form, including dissipation through particle losses.
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quant-ph
|
Quantum interference between photons from an atomic ensemble and a
remote atomic ion: Advances in the distribution of quantum information will likely require
entanglement shared across a hybrid quantum network. Many entanglement
protocols require the generation of indistinguishable photons between the
various nodes of the network. This is challenging in a hybrid environment due
to typically large differences in the spectral and temporal characteristics of
single photons generated in different systems. Here we show, for the first
time, quantum interference between photons generated from a single atomic ion
and an atomic ensemble, located in different buildings and linked via optical
fibre. Trapped ions are leading candidates for quantum computation and
simulation with good matter-to-photon conversion. Rydberg excitations in
neutral-atom ensembles show great promise as interfaces for the storage and
manipulation of photonic qubits with excellent efficiencies. Our measurement of
high-visibility interference between photons generated by these two, disparate
systems is an important building block for the establishment of a hybrid
quantum network.
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quant-ph
|
Geometry and structure of quantum phase space: The application of geometry to physics has provided us with new insightful
information about many physical theories such as classical mechanics, general
relativity, and quantum geometry (quantum gravity). The geometry also plays an
important role in foundations of quantum mechanics and quantum information. In
this work we discuss a geometric framework for mixed quantum states represented
by density matrices, where the quantum phase space of density matrices is
equipped with a symplectic structure, an almost complex structure, and a
compatible Riemannian metric. This compatible triple allow us to investigate
arbitrary quantum systems. We will also discuss some applications of the
geometric framework.
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quant-ph
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Loschmidt echo and dynamical fidelity in periodically driven quantum
systems: We study the dynamical fidelity $\mathcal{F} (t)$ and the Loschmidt echo
$\mathcal{L} (t)$, following a periodic driving of the transverse magnetic
field of a quantum Ising chain (back and forth across the quantum critical
point) by calculating the overlap between the initial ground state and the
state reached after $n$ periods $\tau$. We show that
$\log{\mathcal{F}}(n\tau)/L$ (the logarithm of the fidelity per-site) reaches a
steady value in the asymptotic limit $n\to \infty$, and we derive an exact
analytical expression for this quantity. Remarkably, the steady state value of
$[\log{\mathcal{F}}(n\tau\to \infty)]/L$ shows memory of non-trivial phase
information which is instead hidden in the case of thermodynamic quantities;
this conclusion, moreover, is not restricted to 1-dimensional models.
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quant-ph
|
Communication between inertial observers with partially correlated
reference frames: In quantum communication protocols the existence of a shared reference frame
between two spatially separated parties is normally presumed. However, in many
practical situations we are faced with the problem of misaligned reference
frames. In this paper, we study communication between two inertial observers
who have partial knowledge about the Lorentz transformation that relates their
frames of reference. Since every Lorentz transformation can be decomposed into
a pure boost followed by a rotation, we begin by analysing the effects on
communication when the parties have partial knowledge about the transformation
relating their frames, when the transformation is either a rotation or pure
boost. This then enables us to investigate how the efficiency of communication
is affected due to partially correlated inertial reference frames related by an
arbitrary Lorentz transformation. Furthermore, we show how the results of
previous studies where reference frames are completely uncorrelated are
recovered from our results in appropriate limits.
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quant-ph
|
Autangle: A case of Quantum Narcissism?: In this paper we ask a common psychological question and provide a physics
answer: "Looking into a mirror can one get entangled with one's image?" This is
not a frivolous question; rather, it bears on the effect of boundaries on the
behavior of quantum entanglement between a harmonic oscillator and a quantum
field, a basic problem of interest in proposed mirror-field superposition and
related experiments in macroscopic quantum phenomena, as well as atomic
fluctuation forces near a conducting surface.
The object's internal degree of freedom is modeled by a harmonic oscillator
and the presence of a perfectly reflecting mirror enforces the Dirichlet
boundary conditions on the quantum field, restricting the latter to a half
space. By assuming a bilinear oscillator-field interaction, we derive a coupled
set of equations for the oscillator's and the field's Heisenberg operators. The
former can be cast in the form of a quantum Langevin equation, where the
dissipation and noise kernels respectively correspond to the retarded and
Hadamard functions of the free quantum field in half space.
We use the linear entropy as measures of entanglement between the oscillator
and the quantum field under mirror reflection, then solve the early-time
oscillator-field entanglement dynamics and compare it with that between two
inertial oscillators in free space. At late times when the combined system is
in a stationary state, we obtain exact expressions for the oscillator's
covariance matrix and show that the oscillator-field entanglement decreases as
the oscillator moves closer to the mirror. We explain this behavior
qualitatively with the help of a mirror image and provide an answer to the
question raised above. We also compare this situation with the case of two real
oscillators and explain the differences.
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quant-ph
|
Quantum key distribution using polarized coherent states: We discuss a continuous variables method of quantum key distribution
employing strongly polarized coherent states of light. The key encoding is
performed using the variables known as Stokes parameters, rather than the field
quadratures. Their quantum counterpart, the Stokes operators $\hat{S}_i$
(i=1,2,3), constitute a set of non-commuting operators, being the precision of
simultaneous measurements of a pair of them limited by an uncertainty-like
relation. Alice transmits a conveniently modulated two-mode coherent state, and
Bob randomly measures one of the Stokes parameters of the incoming beam. After
performing reconciliation and privacy amplification procedures, it is possible
to distill a secret common key. We also consider a non-ideal situation, in
which coherent states with thermal noise, instead of pure coherent states, are
used for encoding.
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quant-ph
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Refined Belief Propagation Decoding of Sparse-Graph Quantum Codes: Quantum stabilizer codes constructed from sparse matrices have good
performance and can be efficiently decoded by belief propagation (BP). A
conventional BP decoding algorithm treats binary stabilizer codes as additive
codes over GF(4). This algorithm has a relatively complex process of handling
check-node messages, which incurs higher decoding complexity. Moreover, BP
decoding of a stabilizer code usually suffers a performance loss due to the
many short cycles in the underlying Tanner graph. In this paper, we propose a
refined BP decoding algorithm for quantum codes with complexity roughly the
same as binary BP. For a given error syndrome, this algorithm decodes to the
same output as the conventional quaternary BP but the passed node-to-node
messages are single-valued, unlike the quaternary BP, where multivalued
node-to-node messages are required. Furthermore, the techniques of message
strength normalization can naturally be applied to these single-valued messages
to improve the performance. Another observation is that the message-update
schedule affects the performance of BP decoding against short cycles. We show
that running BP with message strength normalization according to a serial
schedule (or other schedules) may significantly improve the decoding
performance and error floor in computer simulation.
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quant-ph
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Detuning modulated universal composite pulses: We present a general method to derive detuning-modualted composite pulses
(DMCPs) as N rotations of a canonical two-state quantum system to create
accurate and robust pulses that are independent of the initial state of the
system. This scheme has minimal pulse overhead, and achieves pulses that are
stable against amplitude errors well within the $10^{-4}$ threshold that may be
suitable for quantum information processing (QIP), within the lifetime of the
system. This family of pulses enables to overcome inevitable fabrication errors
in silicon photonics, and relax the need for a precise initial state of light
coupled into the system to achieve accurate light transfer. Furthermore, we
extend universal DMCPs to n-level systems with irreducible SU(2) symmetry to
create state transfer that is highly robust to errors in the pulse area from
any initial state.
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quant-ph
|
Economical Quantum Secure Direct Communication Network with Single
Photons: A scheme for quantum secure direct communication (QSDC) network is proposed
with a sequence of polarized single photons. The single photons are prepared
originally in the same state |0> by the servers on the network, which will
reduce the difficulty for the legitimate users to check eavesdropping largely.
The users code the information on the single photons with two unitary
operations which do not change their measuring bases. Some decoy photons, which
are produced by operating the sample photons with a Hadamard, are used for
preventing a potentially dishonest server from eavesdropping the quantum lines
freely. This scheme is an economical one as it is the easiest way for QSDC
network communication securely.
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quant-ph
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Adiabatic Transparency of Multilevel Atomic Media for Short
High-intensity Pulses: We consider a medium of multilevel atomic systems interacting with radiation
pulses. A relatively simple technique of analytic calculations is proposed,
which allows revealing all necessary conditions (with sufficient conditions to
be checked separately) imposed on the interaction parameters, for which the
mean dipole moment of a multilevel atomic medium vanishes, i.e., the medium
becomes transparent via adiabatic interaction. The proposed technique is based
on the method of quasienergies and illustrated for three- and five-level atomic
systems. The necessary conditions for the propagation length where the
interaction adiabaticity is preserved in the medium are obtained.
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quant-ph
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Finite key effects in satellite quantum key distribution: Global quantum communications will enable long-distance secure data transfer,
networked distributed quantum information processing, and other
entanglement-enabled technologies. Satellite quantum communication overcomes
optical fibre range limitations, with the first realisations of satellite
quantum key distribution (SatQKD) being rapidly developed. However, limited
transmission times between satellite and ground station severely constrains the
amount of secret key due to finite-block size effects. Here, we analyse these
effects and the implications for system design and operation, utilising
published results from the Micius satellite to construct an empirically-derived
channel and system model for a trusted-node downlink employing efficient BB84
weak coherent pulse decoy states with optimised parameters. We quantify
practical SatQKD performance limits and examine the effects of link efficiency,
background light, source quality, and overpass geometries to estimate long-term
key generation capacity. Our results may guide design and analysis of future
missions, and establish performance benchmarks for both sources and detectors.
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quant-ph
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Beyond Shannon Limits: Quantum Communications through Quantum Paths: A crucial step towards the 6th generation (6G) of networks would be a shift
in communication paradigm beyond the limits of Shannon's theory. In both
classical and quantum Shannon's information theory, communication channels are
generally assumed to combine through classical trajectories, so that the
associated network path traversed by the information carrier is well-defined.
Counter-intuitively, quantum mechanics enables a quantum information carrier to
propagate through a quantum path, i.e., through a path such that the causal
order of the constituting communications channels becomes indefinite. Quantum
paths exhibit astonishing features, such as providing non-null capacity even
when no information can be sent through any classical path. In this paper, we
study the quantum capacity achievable via a quantum path and establish upper
and the lower bounds for it. Our findings reveal the substantial advantage
achievable with a quantum path over any classical placements of communications
channels in terms of ultimate achievable communication rates. Furthermore, we
identify the region where a quantum path incontrovertibly outperforms the
amount of transmissible information beyond the limits of conventional quantum
Shannon's theory, and we quantify this advantage over classical paths through a
conservative estimate.
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quant-ph
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Optimal adaptive control for quantum metrology with time-dependent
Hamiltonians: Quantum metrology has been studied for a wide range of systems with
time-independent Hamiltonians. For systems with time-dependent Hamiltonians,
however, due to the complexity of dynamics, little has been known about quantum
metrology. Here we investigate quantum metrology with time-dependent
Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher
information for parameters in time-dependent Hamiltonians, and show proper
Hamiltonian control is necessary to optimize the Fisher information. We derive
the optimal Hamiltonian control, which is generally adaptive, and the
measurement scheme to attain the optimal Fisher information. In a minimal
example of a qubit in a rotating magnetic field, we find a surprising result
that the fundamental limit of $T^{2}$ time scaling of quantum Fisher
information can be broken with time-dependent Hamiltonians, which reaches
$T^{4}$ in estimating the rotation frequency of the field. We conclude by
considering level crossings in the derivatives of the Hamiltonians, and point
out additional control is necessary for that case.
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quant-ph
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Increasing identical particle entanglement by fuzzy measurements: We investigate the effects of fuzzy measurements on spin entanglement for
identical particles, both fermions and bosons. We first consider an ideal
measurement apparatus and define operators that detect the symmetry of the
spatial and spin part of the density matrix as a function of particle distance.
Then, moving on to realistic devices that can only detect the position of the
particle to within a certain spread, it was surprisingly found that the
entanglement between particles increases with the broadening of detection.
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quant-ph
|
A numerical approach for calculating exact non-adiabatic terms in
quantum dynamics: Understanding how non-adiabatic terms affect quantum dynamics is fundamental
to improving various protocols for quantum technologies. We present a novel
approach to computing the Adiabatic Gauge Potential (AGP), which gives
information on the non-adiabatic terms that arise from time dependence in the
Hamiltonian. Our approach uses commutators of the Hamiltonian to build up an
appropriate basis of the AGP, which can be easily truncated to give an
approximate form when the exact result is intractable. We use this approach to
study the AGP obtained for the transverse field Ising model on a variety of
graphs, showing how the different underlying graph structures can give rise to
very different scaling for the number of terms required in the AGP.
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quant-ph
|
Heisenberg treatment of multiphoton pulses in waveguide QED with
time-delayed feedback: The dynamics of waveguide-QED systems involving coherent time-delayed
feedback give rise to a hierarchy of multi-time correlations within the
Heisenberg picture due to the induced non-Markovianity. We propose to perform a
projection onto a complete set of states in the Hilbert space to decompose the
multi-time correlations into single-time matrix elements. To illustrate the
procedure, we consider the paradigmatic example of a two-level system that
couples to a semi-infinite waveguide and interacts with quantum light pulses.
Our approach complements the range of available methods as it allows
calculating the dynamics under the inclusion of additional dissipation channels
in a numerically exact and efficient manner for multiphoton pulses of arbitrary
shape where memory requirements are known in advance.
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quant-ph
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Proof-of-Concept of Real-World Quantum Key Distribution with Quantum
Frames: We propose and experimentally investigate a fibre-based quantum key
distribution system, which employs polarization qubits encoded into faint laser
pulses. As a novel feature, it allows sending of classical framing information
via sequences of strong laser pulses that precede the quantum data. This allows
synchronization, sender and receiver identification, and compensation of
time-varying birefringence in the communication channel. In addition, this
method also provides a platform to communicate implementation specific
information such as encoding and protocol in view of future optical quantum
networks. Furthermore, we report on our current effort to develop high-rate
error correction.
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quant-ph
|
Arbitrary perfect state transfer in $d$-level spin chains: We exploit a ferromagnetic chain of interacting $d$-level ($d>2$) particles
for arbitrary perfect transfer of quantum states with $(d-1)$ levels. The
presence of one extra degree of freedom in the Hilbert space of particles,
which is not used in encoding, allows to achieve perfect transfer even in a
uniform chain through a repeated measurement procedure with consecutive single
site measurements. Apart from the first iteration, for which the time of
evolution grows linearly with the size of the chain, in all other iterations,
the evolution times are short and does not scale with the length. The success
probability of the mechanism grows with the number of repetitions and
practically after a few iterations the transfer is accomplished with a high
probability.
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quant-ph
|
Quantum mechanics and EPR paradox: The orthodox quantum mechanics has been commonly regarded as being supported
decisively by the polarization EPR experiments, in which Bell's inequalities
have been violated. The given conclusion has been based, however, on several
mistakes that have not been yet commonly known and sufficiently analyzed. The
whole problem will be newly discussed and a corresponding solution will be
proposed.
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quant-ph
|
Point Estimation of States of Finite Quantum Systems: The estimation of the density matrix of a $k$-level quantum system is studied
when the parametrization is given by the real and imaginary part of the entries
and they are estimated by independent measurements. It is established that the
properties of the estimation procedure depend very much on the invertibility of
the true state. In particular, in case of a pure state the estimation is less
efficient. Moreover, several estimation schemes are compared for the unknown
state of a qubit when one copy is measured at a time. It is shown that the
average mean quadratic error matrix is the smallest if the applied observables
are complementary. The results are illustrated by computer simulations.
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quant-ph
|
Construction and Characterization of Symmetrical States for Multiqubit
Systems: A general method in constructing a complete set of wave functions for
multipartite identical qubits is presented based on the irreducible
representations of the permutation group and the nth rank tensors. Particular
examples for n =2, 3, and 4 are derived and the entanglement behavior for each
state is examined from several criteria. It is found that the states so
constructed are all bound entangled states. For the case of even n, all the
states are found to have maximum "n-tangle". The symmetry in spin space is
found to increase the n-tangle in general. The "n-tangle" for n = 4 is found
not always representing 4-way entanglement. It measures the degree of
spin-space symmetry instead. A useful relationship in the classification
between systems containing different number of qubits is given in terms of the
Young's Tableaux based on our analysis.
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quant-ph
|
Applications of the worldline Monte Carlo formalism in quantum mechanics: In recent years efficient algorithms have been developed for the numerical
computation of relativistic single-particle path integrals in quantum field
theory. Here, we adapt this "worldline Monte Carlo" approach to the standard
problem of the numerical approximation of the non-relativistic path integral,
resulting in a formalism whose characteristic feature is the fast,
non-recursive generation of an ensemble of trajectories that is independent of
the potential, and thus universally applicable. The numerical implementation
discretises the trajectories with respect to their time parametrisation but
maintains a continuous spatial domain. In the case of singular potentials, the
discretised action gets adapted to the singularity through a "smoothing"
procedure. We show for a variety of examples (the harmonic oscillator in
various dimensions, the modified P\"oschl-Teller potential, delta-function
potentials, the Coulomb and Yukawa potentials) that the method allows one to
obtain fast and reliable estimates for the Euclidean propagator and use them in
a certain time window suitable for extracting the ground state energy. As an
aside, we apply it for studying the classical limit where nearly classical
trajectories are expected to dominate in the path integral. We expect the
advances made here to be useful also in the relativistic case.
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quant-ph
|
Hermitian versus non-Hermitian representations for minimal length
uncertainty relations: We investigate four different types of representations of deformed canonical
variables leading to generalized versions of Heisenberg's uncertainty relations
resulting from noncommutative spacetime structures. We demonstrate explicitly
how the representations are related to each other and study three
characteristically different solvable models on these spaces, the harmonic
oscillator, the manifestly non-Hermitian Swanson model and an intrinsically
noncommutative model with Poeschl-Teller type potential. We provide an
analytical expression for the metric in terms of quantities specific to the
generic solution procedure and show that when it is appropriately implemented
expectation values are independent of the particular representation. A recently
proposed inequivalent representation resulting from Jordan twists is shown to
lead to unphysical models. We suggest an anti-PT-symmetric modification to
overcome this shortcoming.
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quant-ph
|
Probing quantum phases of ultracold atoms in optical lattices by
transmission spectra in cavity QED: Studies of ultracold atoms in optical lattices link various disciplines,
providing a playground where fundamental quantum many-body concepts, formulated
in condensed-matter physics, can be tested in much better controllable atomic
systems, e.g., strongly correlated phases, quantum information processing.
Standard methods to measure quantum properties of Bose-Einstein condensates
(BECs) are based on matter-wave interference between atoms released from traps
which destroys the system. Here we propose a nondestructive method based on
optical measurements, and prove that atomic statistics can be mapped on
transmission spectra of a high-Q cavity. This can be extremely useful for
studying phase transitions between Mott insulator and superfluid states, since
various phases show qualitatively distinct light scattering. Joining the
paradigms of cavity quantum electrodynamics (QED) and ultracold gases will
enable conceptually new investigations of both light and matter at ultimate
quantum levels, which only recently became experimentally possible. Here we
predict effects accessible in such novel setups.
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quant-ph
|
Operation of a planar-electrode ion-trap array with adjustable RF
electrodes: One path to realizing systems of trapped atomic ions suitable for large-scale
quantum computing and simulation is to create a two-dimensional array of ion
traps. Interactions between nearest-neighbouring ions could then be turned on
and off by tuning the ions' relative positions and frequencies. We demonstrate
and characterize the operation of a planar-electrode ion-trap array. Driving
the trap with a network of phase-locked radio-frequency (RF) resonators which
provide independently variable voltage amplitudes we vary the position and
motional frequency of a 40Ca+ ion in two dimensions within the trap array. With
suitable miniaturization of the trap structure, this provides a viable
architecture for large-scale quantum simulations.
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quant-ph
|
Entanglement generation via phase-matched processes: different Bell
states within the linewidth: It is shown, theoretically and experimentally, that at any type-II
spontaneous parametric down-conversion (SPDC) phase matching, the
decoherence-free singlet Bell state is always present within the natural
bandwidth and can be filtered out by a proper spectral selection. Instead of
the frequency selection, one can perform time selection of the two-photon time
amplitude at the output of a dispersive fibre. Applications to quantum
communication are outlined.
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quant-ph
|
Third order nonlinear correlation of the electromagnetic vacuum at
near-infrared frequencies: In recent years, electro-optic sampling, which is based on Pockel's effect
between an electromagnetic mode and a copropagating, phase-matched ultrashort
probe, has been largely used for the investigation of broadband quantum states
of light, especially in the mid-infrared and terahertz frequency range. The use
of two mutually delayed femtosecond pulses at near-infrared frequencies allows
the measurement of quantum electromagnetic radiation in different space-time
points. Their correlation allows therefore direct access to the spectral
content of a broadband quantum state at terahertz frequencies after Fourier
transformation. In this work, we will prove experimentally and theoretically
that when using strongly focused coherent ultrashort probes, the electro-optic
sampling technique can be affected by the presence of a third-order nonlinear
mixing of the probes' electric field at near-infrared frequencies. Moreover, we
will show that these third-order nonlinear phenomena can also influence
correlation measurements of the quantum electromagnetic radiation. We will
prove that the four-wave mixing of the coherent probes' electric field with
their own electromagnetic vacuum at near-infrared frequencies results in the
generation of a higher-order nonlinear correlation term. The latter will be
characterized experimentally, proving its local nature requiring the physical
overlap of the two probes. The parameters regime where higher order nonlinear
correlation results predominant with respect to electro-optic correlation of
terahertz radiation is provided.
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quant-ph
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Weak Values Technique for Velocity Measurements: In a recent letter, Brunner and Simon propose an interferometric scheme using
imaginary weak values with a frequency-domain analysis to outperform standard
interferometry in longitudinal phase shifts [N. Brunner and C. Simon, Phys.
Rev. Lett {\bf105} (2010)]. Here we demonstrate an interferometric scheme
combined with a time-domain analysis to measure longitudinal velocities. The
technique employs the near-destructive interference of non-Fourier limited
pulses, one Doppler shifted due to a moving mirror, in a Michelson
interferometer. We achieve a velocity measurement of 400 fm/s and show our
estimator to be efficient by reaching its Cram\'{e}r-Rao bound.
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quant-ph
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Bridging Visible and Telecom Wavelengths with a Single-Mode Broadband
Photon Pair Source: We present a spectrally decorrelated photon pair source bridging the visible
and telecom wavelength regions. Tailored design and fabrication of a solid-core
photonic crystal fiber (PCF) lead to the emission of signal and idler photons
into only a single spectral and spatial mode. Thus no narrowband filtering is
necessary and the heralded generation of pure photon number states in ultrafast
wave packets at telecom wavelengths becomes possible.
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quant-ph
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Generic Incomparability of Infinite-Dimensional Entangled States: In support of a recent conjecture by Nielsen (1999), we prove that the
phenomena of 'incomparable entanglement'--whereby, neither member of a pair of
pure entangled states can be transformed into the other via local operations
and classical communication (LOCC)--is a generic feature when the states at
issue live in an infinite-dimensional Hilbert space.
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quant-ph
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Landau levels on the 2D torus: a numerical approach: A numerical method is presented which allows to compute the spectrum of the
Schroedinger operator for a particle constrained on a two dimensional flat
torus under the combined action of a transverse magnetic field and any
conservative force. The method employs a fast Fourier transform to accurately
represent the momentum variables and takes into account the twisted boundary
conditions required by the presence of the magnetic field. An accuracy of
twelve digits is attained even with coarse grids. Landau levels are reproduced
in the case of a uniform field satisfying Dirac's condition. A new fine
structure of levels within the single Landau level is formed when the field has
a sinusoidal component with period commensurable to the integer magnetic
charge.
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quant-ph
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Constraints on the mixing of states on bipartite quantum systems: We give necessary conditions for the mixing problem in bipartite case, which
are independent of eigenvalues and based on algebraic-geometric invariants of
the bipartite states. One implication of our results is that for some special
bipartite mixed states, only special mixed states in a measure zero set can be
used to mix to get them. The results indicate for many physical problems on
composite quantum systems the description based on majorization of eigenvalues
is not sufficient
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quant-ph
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Remote Creation of Quantum Coherence: We study remote creation of coherence (RCC) for a quantum system, A, with the
help of quantum operations on another system, B, and one-way classical
communication.We show that all the nonincoherent quantum states are useful for
RCC and all the incoherent-quantum states are not. The necessary and sufficient
conditions of RCC for the quantum operations on system B are presented for pure
states. The upper bound of average RCC is derived, giving a relation among the
entanglement (concurrence), the RCC of the given quantum state, and the RCC of
the corresponding maximally entangled state. Moreover, for two-qubit systems we
find a simple factorization law for the average remote-created coherence.
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quant-ph
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Regularization of energy-dependent pointlike interactions in 1D quantum
mechanics: We construct a family of hermitian potentials in 1D quantum mechanics that
converges in the zero-range limit to a $\delta$ interaction with an
energy-dependent coupling. It falls out of the standard four-parameter family
of pointlike interactions in 1D. Such classification was made by requiring the
pointlike interaction to be hermitian. But we show that although our
Hamiltonian is hermitian for the standard inner product when the range of the
potential is finite, it becomes hermitian for a different inner product in the
zero-range limit. This inner product attributes a finite probability (and not
probability density) for the particle to be exactly located at the position of
the potential. Such pointlike interactions can then be used to construct
potentials with a finite support with an energy-dependent coupling.
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quant-ph
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On the theory of quantum measurement: The notion of state reduction employed by the standard quantum theory of
measurement is difficult to accept for two reasons: It leaves open where and
when the reduction takes place and it does not give any objective conditions
under which the reduction occurs. Some recently published ideas on this problem
are developed an improved. The disturbance of measurement due to identical
particles in the environment is shown to make any POV measure non-measurable.
Truncated POV (TPOV) measures are introduced that can be measurable if object
systems satisfy the additional requirement of having separation status. The
separation status is generalised from domain of space to domain of phase space.
Starting from the previously introduced distinction between ancillas and
detectors, further study of experiments suggests that a thermodynamic mixing
within a detector and the consequent loss of separation status is the objective
condition for the occurrence of the state reduction. The conjecture is simple,
specific and testable. The theory is illustrated by a model of a real
measurement.
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quant-ph
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Quantum-enhanced reinforcement learning for finite-episode games with
discrete state spaces: Quantum annealing algorithms belong to the class of metaheuristic tools,
applicable for solving binary optimization problems. Hardware implementations
of quantum annealing, such as the quantum annealing machines produced by D-Wave
Systems, have been subject to multiple analyses in research, with the aim of
characterizing the technology's usefulness for optimization and sampling tasks.
Here, we present a way to partially embed both Monte Carlo policy iteration for
finding an optimal policy on random observations, as well as how to embed (n)
sub-optimal state-value functions for approximating an improved state-value
function given a policy for finite horizon games with discrete state spaces on
a D-Wave 2000Q quantum processing unit (QPU). We explain how both problems can
be expressed as a quadratic unconstrained binary optimization (QUBO) problem,
and show that quantum-enhanced Monte Carlo policy evaluation allows for finding
equivalent or better state-value functions for a given policy with the same
number episodes compared to a purely classical Monte Carlo algorithm.
Additionally, we describe a quantum-classical policy learning algorithm. Our
first and foremost aim is to explain how to represent and solve parts of these
problems with the help of the QPU, and not to prove supremacy over every
existing classical policy evaluation algorithm.
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quant-ph
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Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent
and Incoherent Photons Found with Gradient Search: In this work, we consider an environment formed by incoherent photons as a
resource for controlling open quantum systems via an incoherent control. We
exploit a coherent control in the Hamiltonian and an incoherent control in the
dissipator which induces the time-dependent decoherence rates $\gamma_k(t)$
(via time-dependent spectral density of incoherent photons) for generation of
single-qubit gates for a two-level open quantum system which evolves according
to the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation with
time-dependent coefficients determined by these coherent and incoherent
controls. The control problem is formulated as minimization of the objective
functional, which is the sum of Hilbert-Schmidt norms between four fixed basis
states evolved under the GKSL master equation with controls and the same four
states evolved under the ideal gate transformation. The exact expression for
the gradient of the objective functional with respect to piecewise constant
controls is obtained. Subsequent optimization is performed using a gradient
type algorithm with an adaptive step size that leads to oscillating behaviour
of the gradient norm vs iterations. Optimal trajectories in the Bloch ball for
various initial states are computed. A relation of quantum gate generation with
optimization on complex Stiefel manifolds is discussed. We develop methodology
and apply it here for unitary gates as a testing example. The next step is to
apply the method for generation of non-unitary processes and to multi-level
quantum systems.
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quant-ph
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Mechanical effects of optical resonators on driven trapped atoms: Ground
state cooling in a high finesse cavity: We investigate theoretically the mechanical effects of light on atoms trapped
by an external potential, whose dipole transition couples to the mode of an
optical resonator and is driven by a laser. We derive an analytical expression
for the quantum center-of-mass dynamics, which is valid in presence of a tight
external potential. This equation has broad validity and allows for a
transparent interpretation of the individual scattering processes leading to
cooling. We show that the dynamics are a competition of the mechanical effects
of the cavity and of the laser photons, which may mutually interfere. We focus
onto the good-cavity limit and identify novel cooling schemes, which are based
on quantum interference effects and lead to efficient ground state cooling in
experimentally accessible parameter regimes.
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quant-ph
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Preparation of an Exponentially Rising Optical Pulse for Efficient
Excitation of Single Atoms in Free Space: We report on a simple method to prepare optical pulses with exponentially
rising envelope on the time scale of a few ns. The scheme is based on the
exponential transfer function of a fast transistor, which generates an
exponentially rising envelope that is transferred first on a radio frequency
carrier, and then on a coherent cw laser beam with an electro-optical phase
modulator (EOM). The temporally shaped sideband is then extracted with an
optical resonator and can be used to efficiently excite a single Rb-87 atom.
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quant-ph
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Generation of phase-coherent states: An interaction scheme involving nonlinear $\chi^{(2)}$ media is suggested for
the generation of phase-coherent states (PCS). The setup is based on parametric
amplification of vacuum followed by up-conversion of the resulting twin-beam.
The involved nonlinear interactions are studied by the exact numerical
diagonalization. An experimentally achievable working regime to approximate PCS
with high conversion rate is given, and the validity of parametric
approximation is discussed.
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quant-ph
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Precise tomography of optical polarization qubits under conditions of
chromatic aberration of quantum transformations: In this work we present an algorithm of building an adequate model of
polarizing quantum state measurement. This model takes into account chromatic
aberration of the basis change transformation caused by the parasitic
dispersion of the wave plates crystal and finite radiation spectral bandwidth.
We show that the chromatic aberration reduces the amount of information in the
measurements results. Using the information matrix approach we estimate the
impact of this effect on the qubit state reconstruction fidelity for different
values of sample size and spectral bandwidth. We also demonstrate that our
model outperforms the standard model of projective measurements as it could
suppress systematic errors of quantum tomography even when one performs the
measurements using wave plates of high order.
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quant-ph
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Quantum Fields a la Sylvester and Witt: A structural explanation of the coupling constants in the standard model, i.e
the fine structure constant and the Weinberg angle, and of the gauge fixing
contributions is given in terms of symmetries and representation theory. The
coupling constants are normalizations of Lorentz invariantly embedded little
groups (spin and polarization) arising in a harmonic analysis of quantum vector
fields. It is shown that the harmonic analysis of massless fields requires an
extension of the familiar Fourier decomposition, containing also indefinite
unitary nondecomposable time representations. This is illustrated by the
nonprobabilistic contributions in the electromagnetic field.
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quant-ph
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Event-by-event simulation of Einstein-Podolsky-Rosen-Bohm experiments: We construct an event-based computer simulation model of the
Einstein-Podolsky-Rosen-Bohm experiments with photons. The algorithm is a
one-to-one copy of the data gathering and analysis procedures used in real
laboratory experiments. We consider two types of experiments, those with a
source emitting photons with opposite but otherwise unpredictable polarization
and those with a source emitting photons with fixed polarization. In the
simulation, the choice of the direction of polarization measurement for each
detection event is arbitrary. We use three different procedures to identify
pairs of photons and compute the frequency of coincidences by analyzing
experimental data and simulation data. The model strictly satisfies Einstein's
criteria of local causality, does not rely on any concept of quantum theory and
reproduces the results of quantum theory for both types of experiments. We give
a rigorous proof that the probabilistic description of the simulation model
yields the quantum theoretical expressions for the single- and two-particle
expectation values.
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quant-ph
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Motional Quantum Error Correction: We examine the dynamics of a qubit stored in the motional degrees of freedom
of an ultra-cold ion in an ion trap which is subject to the decoherence effects
of a finite-temperature bath. We discover an encoding of the qubit, in two of
the motional modes of the ion, which is stable against the occurrence of either
none or one quantum jump. For the case of a zero-temperature bath we describe
how to transfer only the information concerning the occurrence of quantum jumps
and their types to a measuring apparatus, without affecting the ion's motional
state significantly. We then describe how to generate a unitary restoration of
the qubit given the jump information, through Raman processes generated by a
series of laser pulses.
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quant-ph
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Machine learning quantum states in the NISQ era: We review the development of generative modeling techniques in machine
learning for the purpose of reconstructing real, noisy, many-qubit quantum
states. Motivated by its interpretability and utility, we discuss in detail the
theory of the restricted Boltzmann machine. We demonstrate its practical use
for state reconstruction, starting from a classical thermal distribution of
Ising spins, then moving systematically through increasingly complex pure and
mixed quantum states. Intended for use on experimental noisy intermediate-scale
quantum (NISQ) devices, we review recent efforts in reconstruction of a cold
atom wavefunction. Finally, we discuss the outlook for future experimental
state reconstruction using machine learning, in the NISQ era and beyond.
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quant-ph
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Predicting Expressibility of Parameterized Quantum Circuits using Graph
Neural Network: Parameterized Quantum Circuits (PQCs) are essential to quantum machine
learning and optimization algorithms. The expressibility of PQCs, which
measures their ability to represent a wide range of quantum states, is a
critical factor influencing their efficacy in solving quantum problems.
However, the existing technique for computing expressibility relies on
statistically estimating it through classical simulations, which requires many
samples. In this work, we propose a novel method based on Graph Neural Networks
(GNNs) for predicting the expressibility of PQCs. By leveraging the graph-based
representation of PQCs, our GNN-based model captures intricate relationships
between circuit parameters and their resulting expressibility. We train the GNN
model on a comprehensive dataset of PQCs annotated with their expressibility
values. Experimental evaluation on a four thousand random PQC dataset and IBM
Qiskit's hardware efficient ansatz sets demonstrates the superior performance
of our approach, achieving a root mean square error (RMSE) of 0.03 and 0.06,
respectively.
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quant-ph
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Certified quantum random number generator based on single-photon
entanglement: Quantum entanglement represents an ideal resource to guarantee the security
of random numbers employed in many scientific and cryptographic applications.
However, entanglement-based certified random number generators are particularly
challenging to implement. Here, we demonstrate a new certified quantum random
number generator based on momentum-polarization entangled single photon states.
The use of single photon entanglement allows employing an attenuated laser
source and a simple setup where only linear optical components are utilized.
For the latter, a semi-device-independent modeling of the photonic quantum
random number generator is developed, which certifies a minimum entropy of
$(2.5\pm 0.5)\%$, corresponding to a generation rate of 4.4 kHz. At the
expenses of a higher level of trust in the system, the certified minimum
entropy can be increased to $(30.1 \pm0.5 )\%$, implying a generation rate of
52.7 kHz. Our results show that a simple optical implementation combined with
an accurate modeling provide an entanglement-based high-security quantum random
number generator using imperfect devices.
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quant-ph
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Stark-chirped rapid adiabatic passage in the presence of dissipation for
quantum computation: Stark-chirped rapid adiabatic passage (SCRAP) is an important technique used
for coherent quantum controls. In this paper we investigate how the
practically-existing dissipation of the system influences on the efficiency of
the passage, and thus the fidelities of the SCRAP-based quantum gates. With
flux-biased Josephson qubits as a specifical example, our results show clearly
that the efficiency of the logic gates implemented by SCRAP are robust against
the weak dissipation. The influence due to the non-adiabtic transitions between
the adiabatic passages is comparatively significantly small. Therefore, the
SCRAP-based logic gates should be feasible for the realistic physical systems
with noises.
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quant-ph
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Threshold quantum cryptograph based on Grover's algorithm: Grover's operator in the two-qubit case can transform a basis into its
conjugated basis. A permutation operator can transform a state in the two
conjugated bases into its orthogonal state. These properties are included in a
threshold quantum protocol. The proposed threshold quantum protocol is secure
based the proof that the legitimate participators can only eavesdrop 2 bits of
3 bits operation information on one two-qubit with error probability 3/8. We
propose a scheme to detect the Trojan horse attack without destroying the legal
qubit.
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quant-ph
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One-dimensional atomic superfluids as a model system for quantum
thermodynamics: In this chapter we will present the one-dimensional (1d) quantum degenerate
Bose gas (1d superfluid) as a testbed to experimentally illustrate some of the
key aspects of quantum thermodynamics. Hard-core bosons in one-dimension are
described by the integrable Lieb-Lininger model. Realistic systems, as they can
be implemented, are only approximately integrable, and let us investigate the
cross over to 'thermalisation'. They show such fundamental properties as
pre-thermalisation, general Gibbs ensembles and light-cone like spreading of
de-coherence. On the other hand they are complex enough to illustrate that our
limited ability to measure only (local) few-body observables determines the
relevant description of the many-body system and its physics. One consequence
is the observation of quantum recurrences in systems with thousand of
interacting particles. The relaxation observed in 1D superfluids is universal
for a large class of many-body systems, those where the relevant physics can be
described by a set of 'long lived' collective modes. The time window where the
'close to integrable' dynamics can be observed is given by the 'lifetime' of
the quasi-particles associated with the collective modes. Based on these
observations one can view (in a quantum field theory sense) a many-body quantum
system at T=0 as 'vacuum' and its excitations as the system to experiment with.
This viewpoint leads to a new way to build thermal machines from the
quasi-particles in 1D superfluids. We will give examples of how to realise
these systems and point to a few interesting questions that might be addressed.
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quant-ph
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Continuous Transitions Between Quantum and Classical Electrodynamics: The Maxwell equations in the presence of sources are first derived without
making use of the potentials and the Hamilton-Jacobi equation for classical
electrodynamics is written down. The manifestly gauge invariant theory is then
quantized to write down the Hamilton-Jacobi equation in quantum
electrodynamics. Finally, an interpolating field theory is proposed that
describes continuous transitions between quantum and classical electrodynamics.
It is shown that energy flow lines are identical for quantum and classical
fields in the case of the double-slit arrangement but differ in the case of
vortex beams.
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quant-ph
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Amplification of quadratic Hamiltonians: Speeding up the dynamics of a quantum system is of paramount importance for
quantum technologies. However, in finite dimensions and without full knowledge
of the details of the system, it is easily shown to be impossible. In contrast
we show that continuous variable systems described by a certain class of
quadratic Hamiltonians can be sped up without such detailed knowledge. We call
the resultant procedure Hamiltonian amplification (HA). The HA method relies on
the application of local squeezing operations allowing for amplifying even
unknown or noisy couplings and frequencies by acting on individual modes.
Furthermore, we show how to combine HA with dynamical decoupling to achieve
amplified Hamiltonians that are free from environmental noise. Finally, we
illustrate a significant reduction in gate times of cavity resonator qubits as
one potential use of HA.
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quant-ph
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Quantum Networks in Divergence-free Circuit QED: Superconducting circuits are one of the leading quantum platforms for quantum
technologies. With growing system complexity, it is of crucial importance to
develop scalable circuit models that contain the minimum information required
to predict the behaviour of the physical system. Based on microwave engineering
methods, divergent and non-divergent Hamiltonian models in circuit quantum
electrodynamics have been proposed to explain the dynamics of superconducting
quantum networks coupled to infinite-dimensional systems, such as transmission
lines and general impedance environments. Here, we study systematically common
linear coupling configurations between networks and infinite-dimensional
systems. The main result is that the simple Lagrangian models for these
configurations present an intrinsic natural length that provides a natural
ultraviolet cutoff. This length is due to the unavoidable dressing of the
environment modes by the network. In this manner, the coupling parameters
between their components correctly manifest their natural decoupling at high
frequencies. Furthermore, we show the requirements to correctly separate
infinite-dimensional coupled systems in local bases. We also compare our
analytical results with other analytical and approximate methods available in
the literature. Finally, we propose several applications of these general
methods to analog quantum simulation of multi-spin-boson models in
non-perturbative coupling regimes.
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quant-ph
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Learning models of quantum systems from experiments: An isolated system of interacting quantum particles is described by a
Hamiltonian operator. Hamiltonian models underpin the study and analysis of
physical and chemical processes throughout science and industry, so it is
crucial they are faithful to the system they represent. However, formulating
and testing Hamiltonian models of quantum systems from experimental data is
difficult because it is impossible to directly observe which interactions the
quantum system is subject to. Here, we propose and demonstrate an approach to
retrieving a Hamiltonian model from experiments, using unsupervised machine
learning. We test our methods experimentally on an electron spin in a
nitrogen-vacancy interacting with its spin bath environment, and numerically,
finding success rates up to 86%. By building agents capable of learning
science, which recover meaningful representations, we can gain further insight
on the physics of quantum systems.
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quant-ph
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Quantum synchronization due to information backflow: The phase synchronization of a single qubit in a dissipative bath in the
absence of driving field is demonstrated. Using the Husimi $Q$-function we show
that the phase preference is present in the long time limit only during
non-Markovian evolution with a finite detuning. This happens due to the
information backflow signifying that non-Markovianity is a resource for quantum
synchronization. To quantify synchronization we use the shifted phase
distribution as well as its maximal value. From the maximal value of the
shifted phase distribution we observe the signatures of quantum synchronization
{\it viz} the Arnold tongue. In our case the region ofsynchronization is
outside the tongue region and the region inside the tongue is the
desynchronized region. This is in contrast to the results in the literature,
where the synchronization is within the tongue region.
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quant-ph
|
Foundations and Measures of Quantum Non-Markovianity: The basic features of the dynamics of open quantum systems, such as the
dissipation of energy, the decay of coherences, the relaxation to an
equilibrium or non-equilibrium stationary state, and the transport of
excitations in complex structures are of central importance in many
applications of quantum mechanics. The theoretical description, analysis and
control of non-Markovian quantum processes play an important role in this
context. While in a Markovian process an open system irretrievably loses
information to its surroundings, non-Markovian processes feature a flow of
information from the environment back to the open system, which implies the
presence of memory effects and represents the key property of non-Markovian
quantum behavior. Here, we review recent ideas developing a general
mathematical definition for non-Markoviantiy in the quantum regime and a
measure for the degree of memory effects in the dynamics of open systems which
are based on the exchange of information between system and environment. We
further study the dynamical effects induced by the presence of
system-environment correlations in the total initial state and design suitable
methods to detect such correlations through local measurements on the open
system.
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quant-ph
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Simulating Hamiltonian dynamics with a truncated Taylor series: We describe a simple, efficient method for simulating Hamiltonian dynamics on
a quantum computer by approximating the truncated Taylor series of the
evolution operator. Our method can simulate the time evolution of a wide
variety of physical systems. As in another recent algorithm, the cost of our
method depends only logarithmically on the inverse of the desired precision,
which is optimal. However, we simplify the algorithm and its analysis by using
a method for implementing linear combinations of unitary operations to directly
apply the truncated Taylor series.
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quant-ph
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Experimental demonstration of quantum effects in the operation of
microscopic heat engines: The heat engine, a machine that extracts useful work from thermal sources, is
one of the basic theoretical constructs and fundamental applications of
classical thermodynamics. The classical description of a heat engine does not
include coherence in its microscopic degrees of freedom. By contrast, a quantum
heat engine might possess coherence between its internal states. Although the
Carnot efficiency cannot be surpassed, and coherence can be performance
degrading in certain conditions, it was recently predicted that even when using
only thermal resources, internal coherence can enable a quantum heat engine to
produce more power than any classical heat engine using the same resources.
Such a power boost therefore constitutes a quantum thermodynamic signature. It
has also been shown that the presence of coherence results in the thermodynamic
equivalence of different quantum heat engine types, an effect with no classical
counterpart. Microscopic heat machines have been recently implemented with
trapped ions, and proposals for heat machines using superconducting circuits
and optomechanics have been made. When operated with standard thermal baths,
however, the machines implemented so far have not demonstrated any inherently
quantum feature in their thermodynamic quantities. Here we implement two types
of quantum heat engines by use of an ensemble of nitrogen-vacancy centres in
diamond, and experimentally demonstrate both the coherence power boost and the
equivalence of different heat-engine types. This constitutes the first
observation of quantum thermodynamic signatures in heat machines.
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quant-ph
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Efficient Unitarity Randomized Benchmarking of Few-qubit Clifford Gates: Unitarity randomized benchmarking (URB) is an experimental procedure for
estimating the coherence of implemented quantum gates independently of state
preparation and measurement errors. These estimates of the coherence are
measured by the unitarity. A central problem in this experiment is relating the
number of data points to rigorous confidence intervals. In this work we provide
a bound on the required number of data points for Clifford URB as a function of
confidence and experimental parameters. This bound has favorable scaling in the
regime of near-unitary noise and is asymptotically independent of the length of
the gate sequences used. We also show that, in contrast to standard randomized
benchmarking, a nontrivial number of data points is always required to overcome
the randomness introduced by state preparation and measurement errors even in
the limit of perfect gates. Our bound is sufficiently sharp to benchmark
small-dimensional systems in realistic parameter regimes using a modest number
of data points. For example, we show that the unitarity of single-qubit
Clifford gates can be rigorously estimated using few hundred data points under
the assumption of gate-independent noise. This is a reduction of orders of
magnitude compared to previously known bounds.
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quant-ph
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Error mitigation with Clifford quantum-circuit data: Achieving near-term quantum advantage will require accurate estimation of
quantum observables despite significant hardware noise. For this purpose, we
propose a novel, scalable error-mitigation method that applies to gate-based
quantum computers. The method generates training data
$\{X_i^{\text{noisy}},X_i^{\text{exact}}\}$ via quantum circuits composed
largely of Clifford gates, which can be efficiently simulated classically,
where $X_i^{\text{noisy}}$ and $X_i^{\text{exact}}$ are noisy and noiseless
observables respectively. Fitting a linear ansatz to this data then allows for
the prediction of noise-free observables for arbitrary circuits. We analyze the
performance of our method versus the number of qubits, circuit depth, and
number of non-Clifford gates. We obtain an order-of-magnitude error reduction
for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and
on a 64-qubit noisy simulator.
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quant-ph
|
Direct detection of quantum non-Gaussian light from a dispersively
coupled single atom: Many applications in quantum communication, sensing and computation need
provably quantum non-Gaussian light. Recently such light, witnessed by a
negative Wigner function, has been estimated using homodyne tomography from a
single atom dispersively coupled to a high-finesse cavity. This opens an
investigation of quantum non-Gaussian light for many experiments with atoms and
solid-state emitters. However, at their early stage, an atom or emitter in a
cavity system with different channels to the environment and additional noise
are insufficient to produce negative Wigner functions. Moreover, homodyne
detection is frequently challenging for such experiments. We analyse these
issues and prove that such cavities can be used to emit quantum non-Gaussian
light employing single-photon detection in the Hanbury Brown and Twiss
configuration and quantum non-Gaussianity criteria suitable for this
measurement. We investigate in detail cases of considerable cavity leakage when
the negativity of the Wigner function disappears completely. Advantageously,
quantum non-Gaussian light can be still conclusively proven for a large set of
the cavity parameters at the cost of overall measurement time, even if noise is
present.
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quant-ph
|
Quantum algorithm to distinguish Boolean functions of different weights: We exploit Grover operator of database search algorithm for weight decision
algorithm. In this research, weight decision problem is to find an exact weight
w from given two weights as w1 and w2 where w1+w2=1 and 0<w1<w2<1. Firstly, if
a Boolean function is given and when weights are {1/4,3/4}, we can find w with
only one application of Grover operator. Secondly, if we apply k many times of
Grover operator, we can decide w from the set of weights
{sin^2(\frac{k}{2k+1}\frac{\pi}{2}) cos^2(\frac{k}{2k+1}\frac{\pi}{2})}.
Finally, by changing the last two Grover operators with two phase conditions,
we can decide w from given any set of two weights. To decide w with a sure
success, if the quantum algorithm requires O(k) Grover steps, then the best
known classical algorithm requires \Omega(k^s) steps where s>2. Hence the
quantum algorithm achieves at least quadratic speedup.
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quant-ph
|
Ultra-bright source of polarization-entangled photons: Using the process of spontaneous parametric down conversion in a novel
two-crystal geometry, one can generate a source of polarization-entangled
photon pairs which is orders of magnitude brighter than previous sources. We
have measured a high level of entanglement between photons emitted over a
relatively large collection angle, and over a 10-nm bandwidth. As a
demonstration of the source intensity, we obtained a 242-$\sigma$ violation of
Bell's inequalities in less than three minutes.
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quant-ph
|
Rank Reduction for the Local Consistency Problem: We address the problem of how simple a solution can be for a given quantum
local consistency instance. More specifically, we investigate how small the
rank of the global density operator can be if the local constraints are known
to be compatible. We prove that any compatible local density operators can be
satisfied by a low rank global density operator. Then we study both fermionic
and bosonic versions of the N-representability problem as applications. After
applying the channel-state duality, we prove that any compatible local channels
can be obtained through a global quantum channel with small Kraus rank.
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quant-ph
|
Quantum communication networks with defects in silicon carbide: Quantum communication promises unprecedented communication capabilities
enabled by the transmission of quantum states of light. However, current
implementations face severe limitations in communication distance due to photon
loss. Silicon carbide (SiC) defects have emerged as a promising quantum device
platform, offering strong optical transitions, long spin coherence lifetimes
and the opportunity for integration with semiconductor devices. Some defects
with optical transitions in the telecom range have been identified, allowing to
interface with fiber networks without the need for wavelength conversion. These
unique properties make SiC an attractive platform for the implementation of
quantum nodes for quantum communication networks. We provide an overview of the
most prominent defects in SiC and their implementation in spin-photon
interfaces. Furthermore, we model a memory-enhanced quantum communication
protocol in order to extract the parameters required to surpass a direct
point-to-point link performance. Based on these insights, we summarize the key
steps required towards the deployment of SiC devices in large-scale quantum
communication networks.
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quant-ph
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Measurements of non local weak values: Some recent attempts at measuring non local weak values via local
measurements are discussed and shown to be less robust than standard weak
measurements. A method for measuring some non local weak values via non local
measurements (non local weak measurements) is introduced. The meaning of non
local weak values is discussed.
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quant-ph
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Optimum topology of quasi-one dimensional nonlinear optical quantum
systems: We determine the optimum topology of quasi-one dimensional nonlinear optical
structures using generalized quantum graph models. Quantum graphs are
relational graphs endowed with a metric and a multiparticle Hamiltonian acting
on the edges, and have a long application history in aromatic compounds,
mesoscopic and artificial materials, and quantum chaos. Quantum graphs have
recently emerged as models of quasi-one dimensional electron motion for
simulating quantum-confined nonlinear optical systems. This paper derives the
nonlinear optical properties of quantum graphs containing the basic star vertex
and compares their responses across topological and geometrical classes. We
show that such graphs have exactly the right topological properties to generate
energy spectra required to achieve large, intrinsic optical nonlinearities. The
graphs have the exquisite geometrical sensitivity required to tune wave
function overlap in a way that optimizes the transition moments. We show that
this class of graphs consistently produces intrinsic optical nonlinearities
near the fundamental limits. We discuss the application of the models to the
prediction and development of new nonlinear optical structures.
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quant-ph
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Proposal to use Humans to switch settings in a Bell experiment: In this paper I discuss how we might go about about performing a Bell
experiment in which humans are used to decide the settings at each end. To get
a sufficiently high rate of switching at both ends, I suggest an experiment
over a distance of about 100km with 100 people at each end wearing EEG
headsets, with the signals from these headsets being used to switch the
settings.
The radical possibility we wish to investigate is that, when humans are used
to decide the settings (rather than various types of random number generators),
we might then expect to see a violation of Quantum Theory in agreement with the
relevant Bell inequality. Such a result, while very unlikely, would be
tremendously significant for our understanding of the world (and I will discuss
some interpretations).
Possible radical implications aside, performing an experiment like this would
push the development of new technologies. The biggest problem would be to get
sufficiently high rates wherein there has been a human induced switch at each
end before a signal as to the new value of the setting could be communicated to
the other end and, at the same time, a photon pair is detected. It looks like
an experiment like this, while challenging, is just about feasible with current
technologies.
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quant-ph
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Complexity of D-dimensional hydrogenic systems in position and momentum
spaces: The internal disorder of a D-dimensional hydrogenic system, which is strongly
associated to the non-uniformity of the quantum-mechanical density of its
physical states, is investigated by means of the shape complexity in the two
reciprocal spaces. This quantity, which is the product of the disequilibrium or
averaging density and the Shannon entropic power, is mathematically expressed
for both ground and excited stationary states in terms of certain entropic
functionals of Laguerre and Gegenbauer (or ultraspherical) polynomials. We
emphasize the ground and circular states, where the complexity is explicitly
calculated and discussed by means of the quantum numbers and dimensionality.
Finally, the position and momentum shape complexities are numerically discussed
for various physical states and dimensionalities, and the dimensional and
Rydberg energy limits as well as their associated uncertainty products are
explicitly given. As a byproduct, it is shown that the shape complexity of the
system in a stationary state does not depend on the strength of the Coulomb
potential involved.
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quant-ph
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Optoelectronic control of atomic bistability with graphene: We explore the emergence and active control of optical bistability in a
two-level atom near a graphene sheet. Our theory incorporates self-interaction
of the optically-driven atom and its coupling to electromagnetic vacuum modes,
both of which are sensitive to the electrically-tunable interband transition
threshold in graphene. We show that electro-optical bistability and hysteresis
can manifest in the intensity, spectrum, and quantum statistics of the light
emitted by the atom, which undergoes critical slow-down to steady-state. The
optically-driven atom-graphene interaction constitutes a platform for active
control of driven atomic systems in quantum coherent control and atomic
physics.
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quant-ph
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Entanglement entropy in the Hypercube networks: We investigate the hypercube networks that their nodes are considered as
quantum harmonic oscillators. The entanglement of the ground state can be used
to quantify the amount of information each part of a network shares with the
rest of the system via quantum fluctuations. Therefore, the Schmidt numbers and
entanglement entropy between two special parts of Hypercube network, can be
calculated. To this aim, first we use the stratification method to rewrite the
adjacency matrix of the network in the stratification basis which is the matrix
representation of the angular momentum. Then the entanglement entropy and
Schmidt number for special partitions are calculated an- alytically by using
the generalized Schur complement method. Also, we calculate the entanglement
entropy between two arbitrary equal subsets (two equal subsets have the same
number of vertices) in H(3, 2) and H(4, 2) numerically, and we give the minimum
and maximum values of entanglement entropy in these two Hypercube network. Then
we can conjecture the minimum and maximum values of entanglement entropy for
equal subsets in H(d, 2).
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quant-ph
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Quantum Hamilton-Jacobi Theory: Quantum canonical transformations have attracted interest since the beginning
of quantum theory. Based on their classical analogues, one would expect them to
provide a powerful quantum tool. However, the difficulty of solving a nonlinear
operator partial differential equation such as the quantum Hamilton-Jacobi
equation (QHJE) has hindered progress along this otherwise promising avenue. We
overcome this difficulty. We show that solutions to the QHJE can be constructed
by a simple prescription starting from the propagator of the associated
Schroedinger equation. Our result opens the possibility of practical use of
quantum Hamilton-Jacobi theory. As an application we develop a surprising
relation between operator ordering and the density of paths around a
semiclassical trajectory.
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quant-ph
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Unique Steady-State Squeezing in a Driven Quantum Rabi Model: Squeezing is essential to many quantum technologies and our understanding of
quantum physics. Here we develop a theory of steady-state squeezing that can be
generated in the closed and open quantum Rabi as well as Dicke model. To this
end, we eliminate the spin dynamics which effectively leads to an abstract
harmonic oscillator whose eigenstates are squeezed with respect to the physical
harmonic oscillator. The generated form of squeezing has the unique property of
time-independent uncertainties and squeezed dynamics, a novel type of quantum
behavior. Such squeezing might find applications in continuous back-action
evading measurements and should already be observable in optomechanical systems
and Coulomb crystals.
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quant-ph
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Banach space formalism of quantum mechanics: This paper presents a generalization of quantum mechanics from conventional
Hilbert space formalism to Banach space one. We construct quantum theory
starting with any complex Banach space beyond a complex Hilbert space, through
using a basic fact that a complex Banach space always admits a semi-inner
product. Precisely, in a complex Banach space $\mathbb{X}$ with a given
semi-inner product, a pure state is defined by Lumer \cite{Lumer1961} to be a
bounded linear functional on the space of bounded operators determined by a
normalized element of $\mathbb{X}$ under the semi-inner product, and then the
state space $\mathcal{S} (\mathbb{X})$ of the system is the weakly closed
convex set spanned by all pure states. Based on Lumer's notion of the state, we
associate a quantum system with a complex Banach space $\mathbb{X}$ equipped
with a fixed semi-inner product, and then define a physical event at a quantum
state $\omega \in \mathcal{S}(\mathbb{X})$ to be a projection $P$ (bounded
operator such that $P^2 =P$) in $\mathbb{X}$ satisfying the positivity
condition $0 \le \omega (P) \le 1,$ and a physical quantity at a quantum state
$\omega$ to be a spectral operator of scalar type with real spectrum so that
the associated spectral projections are all physical events at $\omega.$ The
Born formula for measurement of a physical quantity is the natural pairing of
operators with linear functionals satisfying the probability conservation law.
A time evolution of the system is governed by a one-parameter group of
invertible spectral operators determined by a scalar type operator with the
real spectrum, which satisfies the Schr\"{o}dinger equation. Our formulation is
just a generalization of the Dirac-von Neumann formalism of quantum mechanics
to the Banach space setting. We include some examples for illustration.
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quant-ph
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The Pilot-Wave Perspective on Spin: The alternative pilot-wave theory of quantum phenomena -- associated
especially with Louis de Broglie, David Bohm, and John Bell -- reproduces the
statistical predictions of ordinary quantum mechanics, but without recourse to
special \emph{ad hoc} axioms pertaining to measurement. That (and how) it does
so is relatively straightforward to understand in the case of position
measurements and, more generally, measurements whose outcome is ultimately
registered by the position of a pointer. Despite a widespread belief to the
contrary among physicists, the theory can also account successfully for
phenomena involving spin. The main goal of the paper is to explain how the
pilot-wave theory's account of spin works. Along the way, we provide
illuminating comparisons between the orthodox and pilot-wave accounts of spin
and address some puzzles about how the pilot-wave theory relates to the
important theorems of Kochen and Specker and Bell.
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quant-ph
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Initial correlations in open system's dynamics: The Jaynes-Cummings
model: Employing the trace distance as a measure for the distinguishability of
quantum states, we study the influence of initial correlations on the dynamics
of open systems. We concentrate on the Jaynes-Cummings model for which the
knowledge of the exact joint dynamics of system and reservoir allows the
treatment of initial states with arbitrary correlations. As a measure for the
correlations in the initial state we consider the trace distance between the
system-environment state and the product of its marginal states. In particular,
we examine the correlations contained in the thermal equilibrium state for the
total system, analyze their dependence on the temperature and on the coupling
strength, and demonstrate their connection to the entanglement properties of
the eigenstates of the Hamiltonian. A detailed study of the time dependence of
the distinguishability of the open system states evolving from the thermal
equilibrium state and its corresponding uncorrelated product state shows that
the open system dynamically uncovers typical features of the initial
correlations.
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quant-ph
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NMR studies of quantum chaos in a two-qubit kicked top: Quantum chaotic kicked top model is implemented experimentally in a two qubit
system comprising of a pair of spin-1/2 nuclei using Nuclear Magnetic Resonance
techniques. The essential nonlinear interaction was realized using indirect
spin-spin coupling, while the linear kicks were realized using RF pulses. After
a variable number of kicks, quantum state tomography was employed to
reconstruct the single-qubit density matrices using which we could extract
various measures such as von Neumann entropies, Husimi distributions, and
Lyapunov exponents. These measures enabled the study of correspondence with
classical phase space as well as to probe distinct features of quantum chaos,
such as symmetries and temporal periodicity in the two-qubit kicked top.
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quant-ph
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Measurement As Spontaneous Symmetry Breaking, Non-locality and
Non-Boolean Holism: It is shown that having degenerate ground states over the domain of the
wavefunction of a system is a sufficient condition for a quantum system to act
as a measuring apparatus for the system. Measurements are then instances of
spontaneous symmetry breaking to one of these ground states, induced by
environmental perturbations. Together with non-Boolean holism this constitutes
an optimal formulation of quantum mechanics that does not imply non-locality.
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quant-ph
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Phase-sensitive detection of Bragg scattering at 1D optical lattices: We report on the observation of Bragg scattering at 1D atomic lattices. Cold
atoms are confined by optical dipole forces at the antinodes of a standing wave
generated by the two counter-propagating modes of a laser-driven high-finesse
ring cavity. By heterodyning the Bragg-scattered light with a reference beam,
we obtain detailed information on phase shifts imparted by the Bragg scattering
process. Being deep in the Lamb-Dicke regime, the scattered light is not
broadened by the motion of individual atoms. In contrast, we have detected
signatures of global translatory motion of the atomic grating.
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quant-ph
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Fluctuations of work in realistic equilibrium states of quantum systems
with conserved quantities: The out-of-equilibrium dynamics of quantum systems is one of the most
fascinating problems in physics, with outstanding open questions on issues such
as relaxation to equilibrium. An area of particular interest concerns few-body
systems, where quantum and thermal fluctuations are expected to be especially
relevant. In this contribution, we present numerical results demonstrating the
impact of conserved quantities (or 'charges') in the outcomes of
out-of-equilibrium measurements starting from realistic equilibrium states on a
few-body system implementing the Dicke model.
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quant-ph
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Tracking down localized modes in PT-symmetric Hamiltonians under the
influence of a competing nonlinearity: The relevance of parity and time reversal (PT)-symmetric structures in
optical systems is known for sometime with the correspondence existing between
the Schrodinger equation and the paraxial equation of diffraction where the
time parameter represents the propagating distance and the refractive index
acts as the complex potential. In this paper, we systematically analyze a
normalized form of the nonlinear Schrodinger system with two new families of
PT-symmetric potentials in the presence of competing nonlinearities. We
generate a class of localized eigenmodes and carry out a linear stability
analysis on the solutions. In particular, we find an interesting feature of
bifurcation charaterized by the parameter of perturbative growth rate passing
through zero where a transition to imaginary eigenvalues occurs.
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quant-ph
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Bell's Theorem and Entangled Solitons: Entangled solitons construction being introduced in the nonlinear spinor
field model, the Einstein|Podolsky|Rosen (EPR) spin correlation is calculated
and shown to coincide with the quantum mechanical one for the 1/2-spin
particles.
|
quant-ph
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Thermally-activated non-local amplification in quantum energy transport: We study energy-transport efficiency in light-harvesting planar and 3D
complexes of two-level atomic quantum systems, embedded in a common thermal
blackbody radiation. We show that the collective non-local dissipation induced
by the thermal bath plays a fundamental role in energy transport. It gives rise
to a dramatic enhancement of the energy-transport efficiency, which may largely
overcome $100\%$. This effect, which improves the understanding of transport
phenomena in experimentally relevant complexes, suggests a particularly
promising mechanism for quantum energy management.
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quant-ph
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Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation
Values: Many quantum algorithms involve the evaluation of expectation values. Optimal
strategies for estimating a single expectation value are known, requiring a
number of state preparations that scales with the target error $\varepsilon$ as
$\mathcal{O}(1/\varepsilon)$. In this paper, we address the task of estimating
the expectation values of $M$ different observables, each to within additive
error $\varepsilon$, with the same $1/\varepsilon$ dependence. We describe an
approach that leverages Gily\'en et al.'s quantum gradient estimation algorithm
to achieve $\mathcal{O}(\sqrt{M}/\varepsilon)$ scaling up to logarithmic
factors, regardless of the commutation properties of the $M$ observables. We
prove that this scaling is worst-case optimal in the high-precision regime if
the state preparation is treated as a black box, even when the operators are
mutually commuting. We highlight the flexibility of our approach by presenting
several generalizations, including a strategy for accelerating the estimation
of a collection of dynamic correlation functions.
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quant-ph
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On the Evaluation of the electron repulsion integrals: The electron repulsion integrals over the Slater-type orbitals with
non-integer principal quantum numbers are considered. These integrals are
useful in both non-relativistic and relativistic calculations of many-electron
systems. They involve hyper-geometric functions. Due to the non-trivial
structure of infinite series that are used to define them the hyper-geometric
functions are practically difficult to compute. Convergence of their series are
strictly depends on the values of parameters. Computational issues such as
cancellation or round-off error emerge. Relationships free from
hyper$-$geometric functions for expectation values of Coulomb potential
$\left(r_{21}^{-1}\right)$ are derived. These relationships are new and show
that the complication coming from two-range nature of Laplace expansion for the
Coulomb potential is removed. These integrals also form an initial condition
for expectation values of a potential with arbitrary power. The electron
repulsion integrals are expressed by finite series of power functions. The
methodology given here for evaluation of electron repulsion integrals are
adapted to multi-center integrals.
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quant-ph
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Kolmogorov and von Mises viewpoints to the Greenburger-Horne-Zeilinger
paradox: We present comparative probabilistic analysis of the
Greenburger-Horne-Zeilinger paradox in the frameworks of Kolmogorov's
(measure-theoretical) and von Mises' (frequency) models of the probability
theory. This analysis demonstrated that the GHZ paradox is merely a consequence
of the use of Kolmogorov's probabilistic model. By using von Mises' frequency
approach we escape the contradiction between the local realism and quantum
formalism. The frequency approach implies automatically contextual
interpretation of quantum formalism: different collectives induce different
probability distributions. On the other hand, the formal use of Kolmogorov's
model implies the identification of such distributions with one abstract
Kolmogorov measure. In the measure-theoretical approach we can escape the
paradox, if we do not suppose that probability distributions corresponding to
different settings of measurement devices are equivalent. We discuss the
connection between equivalence/singularity dichotomy in measure theory and the
existence of compatible and noncompatible observables.
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quant-ph
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Rogue wavefunctions due to noisy quantum tunneling potentials: In this paper we study the effects of white-noised potentials on nonlinear
quantum tunneling. We use a split-step scheme to numerically solve the
nonlinear Schrodinger equation (NLSE) with a tunneling potential. We consider
three different types of potentials, namely; the single rectangular barrier,
double rectangular barrier and triangular barrier. For all these three cases we
show that white-noise given to potentials do not trigger modulation instability
for tunneling of the sech type soliton solutions of the NLSE. However
white-noised potentials trigger modulation instability for tunneling of the
sinusoidal wavefunctions, thus such a wavefield turns into a chaotic one with
many apparent peaks. We argue that peaks of such a field may be in the form of
rational rogue wave solutions of the NLSE. Our results can be used to examine
the effects of noise on quantum tunneling. Since a rogue wavefunction means a
higher probability of the tunneling particle to be at a given (x,t) coordinate,
our results may also be used for developing the quantum science and technology
with many possible applications including but are not limited to increasing the
resolution and efficiency of scanning tunneling microscopes, enhancing proton
tunneling for DNA mutation and enhancing superconducting properties of
junctions.
|
quant-ph
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Interaction of light and semiconductor can generate quantum states
required for solid state quantum computing: Entangled, steered and other
nonclassical states: Proposals for solid state quantum computing are extremely promising as they
can be used to built room temperature quantum computers. If such a quantum
computer is ever built it would require in-built sources of nonclassical states
required for various quantum information processing tasks. Possibilities of
generation of such nonclassical states are investigated here for a physical
system composed of a monochromatic light coupled to a two-band semiconductor
with direct band gap. The model Hamiltonian includes both photon-exciton and
exciton-exciton interactions. Time evolution of the relevant bosonic operators
are obtained analytically by using a perturbative technique that provides
operator solution for the coupled Heisenberg's equations of motion
corresponding to the system Hamiltonian. The bosonic operators are subsequently
used to study the possibilities of observing single and two mode squeezing and
antibunching after interaction in the relevant modes of light and
semiconductor. Further, entanglement between the exciton and photon modes is
reported. Finally, the nonclassical effects have been studied numerically for
the open quantum system scenario. In this situation, the nonlocal correlations
between two modes are shown to violate EPR steering inequality. The observed
nonclassical features, induced due to exciton-exciton pair interaction, can be
controlled by the phase of input field and the correlations between two modes
are shown to enhance due to nonclassicality in the input field.
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quant-ph
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Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State
Preparation: We propose GM-QAOA, a variation of the Quantum Alternating Operator Ansatz
(QAOA) that uses Grover-like selective phase shift mixing operators. GM-QAOA
works on any NP optimization problem for which it is possible to efficiently
prepare an equal superposition of all feasible solutions; it is designed to
perform particularly well for constraint optimization problems, where not all
possible variable assignments are feasible solutions. GM-QAOA has the following
features: (i) It is not susceptible to Hamiltonian Simulation error (such as
Trotterization errors) as its operators can be implemented exactly using
standard gate sets and (ii) Solutions with the same objective value are always
sampled with the same amplitude.
We illustrate the potential of GM-QAOA on several optimization problem
classes: for permutation-based optimization problems such as the Traveling
Salesperson Problem, we present an efficient algorithm to prepare a
superposition of all possible permutations of $n$ numbers, defined on $O(n^2)$
qubits; for the hard constraint $k$-Vertex-Cover problem, and for an
application to Discrete Portfolio Rebalancing, we show that GM-QAOA outperforms
existing QAOA approaches.
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quant-ph
|
ON THE LARGE ORDER ASYMPTOTICS OF THE WAVE FUNCTION PERTURBATION THEORY: The problem of finding the large order asymptotics for the eigenfunction
perturbation theory in quantum mechanics is studied. The relation between the
wave function argument x and the number of perturbation theory order k that
allows us to construct the asymptotics by saddle-point technique is found:
$x/k^{1/2}=const$, k is large. Classical euclidean solutions starting from the
classical vacuum play an important role in constructing such asymptotics. The
correspondence between the trajectory end and the parameter $x/k^{1/2}$ is
found. The obtained results can be applied to the calculation of the main
values of the observables depending on k in the k-th order of perturbation
theory at larges k and, probably, to the multiparticle production problem.
|
quant-ph
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Manifestations of changes in entanglement and onset of synchronization
in tomograms: Quantum state reconstruction for continuous-variable systems such as the
radiation field poses challenges which arise primarily from the large
dimensionality of the Hilbert space. Many proposals for state reconstruction
exist, ranging from standard reconstruction protocols to applications of
machine learning. No universally applicable protocol exists, however, for
extracting the Wigner function from the optical tomogram of an arbitrary state
of light. We establish that nonclassical effects such as entanglement changes
during dynamical evolution and the onset of quantum synchronization are
mirrored in qualitative changes in optical tomograms themselves, circumventing
the need for state reconstruction for this purpose.
|
quant-ph
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