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Quantum catalysis in cavity QED: Catalysis plays a key role in many scientific areas, most notably in
chemistry and biology. Here we present a catalytic process in a paradigmatic
quantum optics setup, namely the Jaynes-Cummings model, where an atom interacts
with an optical cavity. The atom plays the role of the catalyst, and allows for
the deterministic generation of non-classical light in the cavity. Considering
a cavity prepared in a "classical'' coherent state, and choosing appropriately
the atomic state and the interaction time, we obtain an evolution with the
following properties. First, the state of the cavity has been modified, and now
features non-classicality, as witnessed by sub-Poissonian statistics or Wigner
negativity. Second, the process is catalytic, in the sense that the atom is
deterministically returned to its initial state exactly, and could then in
principle be re-used multiple times. We investigate the mechanism of this
catalytic process, in particular highlighting the key role of correlations and
quantum coherence.
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Enhancing the spin-photon coupling with a micromagnet: Hybrid quantum systems involving solid-state spins and superconducting
microwave cavities play a crucial role in quantum science and technology, but
improving the spin-photon coupling at the single quantum level remains
challenging in such systems. Here, we propose a simple technique to strongly
couple a single solid-state spin to the microwave photons in a superconducting
coplanar waveguide (CPW) cavity via a magnetic microsphere. We show that,
strong coupling at the single spin level can be realized by virtual magnonic
excitations of a nearby micromagnet. The spin-photon coupling strength can be
enhanced up to typically four orders of magnitude larger than that without the
use of the micromagnet. This work can find applications in quantum information
processing with strongly coupled solid-state spin-photonic systems.
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quant-ph
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Formulation of general dynamical invariants and their unitary relations
for time-dependent coupled quantum oscillators: An exact invariant operator of time-dependent coupled oscillators is derived
using the Liouville-von Neumann equation. The unitary relation between this
invariant and the invariant of two uncoupled simple harmonic oscillators is
represented. If we consider the fact that quantum solutions of the simple
harmonic oscillator is well-known, this unitary relation is very useful in
clarifying quantum characteristics of the original systems, such as
entanglement, probability densities, fluctuations of the canonical variables,
and decoherence. We can identify such quantum characteristics by inversely
transforming the mathematical representations of quantum quantities belonging
to the simple harmonic oscillators. As a case in point, the eigenfunctions of
the invariant operator in the original systems are found through inverse
transformation of the well-known eigenfunctions associated with the simple
harmonic oscillators.
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quant-ph
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Correction to the quantum phase operator for photons: The vector potential operator, $\hat{\boldsymbol A}$, is transformed and
rewritten in terms of cosine and sine functions in order to get a clear picture
of how the photon states relate to the $\boldsymbol A$ field. The phase
operator, defined by $\hat E = \exp(-i \hat \phi)$, is derived from this
picture. The result has a close resemblance with the known Susskind-Glogower
(SG) operator, which is given by $\hat E_{SG}=(\hat a_{\boldsymbol k} \hat
a_{\boldsymbol k}^\dagger)^{-1/2} \hat a_{\boldsymbol k}$. It will be shown
that $\hat a_{\boldsymbol k}$ should be replaced by $(\hat a_{\boldsymbol k} +
\hat a_{-\boldsymbol k}^\dagger)$ instead to yield $\hat E = ((\hat
a_{\boldsymbol k} + \hat a_{-\boldsymbol k}^\dagger ) (\hat a_{\boldsymbol
k}^\dagger + \hat a_{-\boldsymbol k}))^{-1/2} (\hat a_{\boldsymbol k} + \hat
a_{-\boldsymbol k}^\dagger)$, which makes the operator unitary. $\hat E$ will
also be analyzed when restricted to the space of only forward moving photons
with wave vector $\boldsymbol k$. The resulting phase operator, $\hat E_+$,
will turn out to resemble the SG operator as well, but with a small correction:
Whereas $E_{SG}$ can be equivalently written as $\hat E_{SG} =
\sum_{n=0}^{\infty} |n\rangle \langle n+1 |$, the operator, $\hat E_+$, is
instead given by $\hat E_+ = \sum_{n=0}^{\infty} a_n |n \rangle \langle n+1|$,
where $a_n = (n+1/2)!/(n! \sqrt{n+1})$. The sequence, $(a_n)_{n \in \lbrace 0,
1, 2, \ldots \rbrace}$, converges to $1$ from below for $n$ going to infinity.
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Fully device independent Conference Key Agreement: We present the first security analysis of conference key agreement (CKA) in
the most adversarial model of device independence (DI). Our protocol can be
implemented {by any experimental setup} that is capable of performing Bell
tests (specifically, we introduce the "Parity-CHSH" inequality), and security
can in principle be obtained for any violation of the Parity-CHSH inequality.
We use a direct connection between the $N$-partite Parity-CHSH inequality and
the CHSH inequality. Namely, the Parity-CHSH inequality can be considered as a
CHSH inequality or another CHSH inequality (equivalent up to relabelling)
depending on the parity of the output of $N-2$ of the parties. We compare the
asymptotic key rate for DICKA to the case where the parties use $N-1$ DIQKD
protocols in order to generate a common key. We show that for some regime of
noise the DICKA protocol leads to better rates.
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quant-ph
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Invertible condition of quantum Fisher information matrix for a mixed
qubit: Estimating multiparamter simultaneously as precise as possible is an
important goal of quantum metrolo- gy. As a first step to this end, here we
give a condition determining whether two arbitrary parameters can be estimated
simultaneously for a qubit in the mixed state. An application of this condition
is shown.
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quant-ph
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The measurement problem revisited: It has been realized that the measurement problem of quantum mechanics is
essentially the determinate-experience problem, and in order to solve the
problem, the physical state representing the measurement result is required to
be also the physical state on which the mental state of an observer supervenes.
This necessitates a systematic analysis of the forms of psychophysical
connection in the solutions to the measurement problem. In this paper, I
propose a new, mentalistic formulation of the measurement problem which lays
more stress on psychophysical connection. By this new formulation, it can be
seen more clearly that the three main solutions to the measurement problem,
namely Everett's theory, Bohm's theory and collapse theories, correspond to
three different forms of psychophysical connection. I then analyze these forms
of psychophysical connection. It is argued that the forms of psychophysical
connection required by Everett's and Bohm's theories have potential problems,
while an analysis of how the mental state of an observer supervenes on her wave
function may help solve the structured tails problem of collapse theories.
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quant-ph
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The Round Complexity of Local Operations and Classical Communication
(LOCC) in Random-Party Entanglement Distillation: A powerful operational paradigm for distributed quantum information
processing involves manipulating pre-shared entanglement by local operations
and classical communication (LOCC). The LOCC round complexity of a given task
describes how many rounds of classical communication are needed to complete the
task. Despite some results separating one-round versus two-round protocols,
very little is known about higher round complexities. In this paper, we revisit
the task of one-shot random-party entanglement distillation as a way to
highlight some interesting features of LOCC round complexity. We first show
that for random-party distillation in three qubits, the number of communication
rounds needed in an optimal protocol depends on the entanglement measure used;
for the same fixed state some entanglement measures need only two rounds to
maximize whereas others need an unbounded number of rounds. In doing so, we
construct a family of LOCC instruments that require an unbounded number of
rounds to implement. We then prove explicit tight lower bounds on the LOCC
round number as a function of distillation success probability. Our
calculations show that the original W-state random distillation protocol by
Fortescue and Lo is essentially optimal in terms of round complexity.
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quant-ph
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Discrete coherent and squeezed states of many-qudit systems: We consider the phase space for a system of $n$ identical qudits (each one of
dimension $d$, with $d$ a primer number) as a grid of $d^{n} \times d^{n}$
points and use the finite field $GF(d^{n})$ to label the corresponding axes.
The associated displacement operators permit to define $s$-parametrized
quasidistribution functions in this grid, with properties analogous to their
continuous counterparts. These displacements allow also for the construction of
finite coherent states, once a fiducial state is fixed. We take this reference
as one eigenstate of the discrete Fourier transform and study the factorization
properties of the resulting coherent states. We extend these ideas to include
discrete squeezed states, and show their intriguing relation with entangled
states between different qudits.
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quant-ph
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Quantumness of gravitational field: A perspective on monogamy relation: Understanding the phenomenon of quantum superposition of gravitational fields
induced by massive quantum particles is an important starting point for quantum
gravity. The purpose of this study is to deepen our understanding of the
phenomenon of quantum superposition of gravitational fields. To this end, we
consider a trade-off relation of entanglement (monogamy relation) in a
tripartite system consisting of two massive particles and a gravitational field
that may be entangled with each other. Consequently, if two particles cannot
exchange information mutually, they are in a separable state, and the particle
and gravitational field are always entangled. Furthermore, even when two
particles can send information to each other, there is a trade-off between the
two particles and the gravitational field. We also investigate the behavior of
the quantum superposition of the gravitational field using quantum discord. We
find that quantum discord increases depending on the length scale of the
particle superposition. Our results may help understand the relationship
between the quantization of the gravitational field and the meaning of the
quantum superposition of the gravitational field.
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quant-ph
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Quantum advantage with shallow circuits: We prove that constant-depth quantum circuits are more powerful than their
classical counterparts. To this end we introduce a non-oracular version of the
Bernstein-Vazirani problem which we call the 2D Hidden Linear Function problem.
An instance of the problem is specified by a quadratic form q that maps n-bit
strings to integers modulo four. The goal is to identify a linear boolean
function which describes the action of q on a certain subset of n-bit strings.
We prove that any classical probabilistic circuit composed of bounded fan-in
gates that solves the 2D Hidden Linear Function problem with high probability
must have depth logarithmic in n. In contrast, we show that this problem can be
solved with certainty by a constant-depth quantum circuit composed of one- and
two-qubit gates acting locally on a two-dimensional grid.
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quant-ph
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On Hastings' counterexamples to the minimum output entropy additivity
conjecture: Hastings recently reported a randomized construction of channels violating
the minimum output entropy additivity conjecture. Here we revisit his argument,
presenting a simplified proof. In particular, we do not resort to the exact
probability distribution of the Schmidt coefficients of a random bipartite pure
state, as in the original proof, but rather derive the necessary large
deviation bounds by a concentration of measure argument. Furthermore, we prove
non-additivity for the overwhelming majority of channels consisting of a Haar
random isometry followed by partial trace over the environment, for an
environment dimension much bigger than the output dimension. This makes
Hastings' original reasoning clearer and extends the class of channels for
which additivity can be shown to be violated.
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quant-ph
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Bipartite discrimination of independently prepared quantum states as a
counterexample to a parallel repetition conjecture: For distinguishing quantum states sampled from a fixed ensemble, the gap in
bipartite and single-party distinguishability can be interpreted as a
nonlocality of the ensemble. In this paper, we consider bipartite state
discrimination in a composite system consisting of $N$ subsystems, where each
subsystem is shared between two parties and the state of each subsystem is
randomly sampled from a particular ensemble comprising the Bell states. We show
that the success probability of perfectly identifying the state converges to
$1$ as $N\rightarrow\infty$ if the entropy of the probability distribution
associated with the ensemble is less than $1$, even if the success probability
is less than $1$ for any finite $N$. In other words, the nonlocality of the
$N$-fold ensemble asymptotically disappears if the probability distribution
associated with each ensemble is concentrated. Furthermore, we show that the
disappearance of the nonlocality can be regarded as a remarkable counterexample
of a fundamental open question in theoretical computer science, called a
parallel repetition conjecture of interactive games with two classically
communicating players. Measurements for the discrimination task include a
projective measurement of one party represented by stabilizer states, which
enable the other party to perfectly distinguish states that are sampled with
high probability.
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quant-ph
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Ultracold polar molecules as qudits: We discuss how the internal structure of ultracold molecules, trapped in the
motional ground state of optical tweezers, can be used to implement qudits. We
explore the rotational, fine and hyperfine structure of $^{40}$Ca$^{19}$F and
$^{87}$Rb$^{133}$Cs, which are examples of molecules with $^2\Sigma$ and
$^1\Sigma$ electronic ground states, respectively. In each case we identify a
subset of levels within a single rotational manifold suitable to implement a
4-level qudit. Quantum gates can be implemented using two-photon microwave
transitions via levels in a neighboring rotational manifold. We discuss
limitations to the usefulness of molecular qudits, arising from off-resonant
excitation and decoherence. As an example, we present a protocol for using a
molecular qudit of dimension $d=4$ to perform the Deutsch algorithm.
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quant-ph
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Compiling quantamorphisms for the IBM Q Experience: Based on the connection between the categorical derivation of classical
programs from specifications and the category-theoretic approach to quantum
physics, this paper contributes to extending the laws of classical program
algebra to quantum programming. This aims at building correct-by-construction
quantum circuits to be deployed on quantum devices such as those available at
the IBM Q Experience. Quantum circuit reversibility is ensured by minimal
complements, extended recursively. Measurements are postponed to the end of
such recursive computations, termed "quantamorphisms", thus maximising the
quantum effect. Quantamorphisms are classical catamorphisms which, extended to
ensure quantum reversibility, implement quantum cycles (vulg. for-loops) and
quantum folds on lists. By Kleisli correspondence, quantamorphisms can be
written as monadic functional programs with quantum parameters. This enables
the use of Haskell, a monadic functional programming language, to perform the
experimental work. Such calculated quantum programs prepared in Haskell are
pushed through Quipper to the Qiskit interface to IBM Q quantum devices. The
generated quantum circuits - often quite large - exhibit the predicted
behaviour. However, running them on real quantum devices incurs into a
significant amount of errors. As quantum devices are constantly evolving, an
increase in reliability is likely in the near future, allowing for our programs
to run more accurately.
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quant-ph
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Unified approach to the nonlinear Rabi models: An analytical approach is proposed to study the two-photon, two-mode and
intensity-dependent Rabi models. By virtue of the su(1,1) Lie algebra, all of
them can be unified to the same Hamiltonian with $\mathcal{Z}_2$ symmetry.
There exist exact isolated solutions, which are located at the level crossings
between different parities and correspond to eigenstates with finite dimension.
Beyond the exact isolated solutions, the regular spectrum can be achieved by
finding the roots of the G-function. The corresponding eigenstates are of
infinite dimension. It is noteworthy that the expansion coefficients of the
eigenstates present an exponential decay behavior. The decay rate decreases
with increasing coupling strength. When the coupling strength tends to the
spectral collapse point $g \rightarrow \omega / 2$, the decay rate tends to
zero which prevents the convergence of the wave functions. This work paves a
way for the analysis of novel physics in nonlinear quantum optics.
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quant-ph
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Clifford recompilation for faster classical simulation of quantum
circuits: Simulating quantum circuits classically is an important area of research in
quantum information, with applications in computational complexity and
validation of quantum devices. One of the state-of-the-art simulators, that of
Bravyi et al, utilizes a randomized sparsification technique to approximate the
output state of a quantum circuit by a stabilizer sum with a reduced number of
terms. In this paper, we describe an improved Monte Carlo algorithm for
performing randomized sparsification. This algorithm reduces the runtime of
computing the approximate state by the factor $\ell/m$, where $\ell$ and $m$
are respectively the total and non-Clifford gate counts. The main technique is
a circuit recompilation routine based on manipulating exponentiated Pauli
operators. The recompilation routine also facilitates numerical search for
Clifford decompositions of products of gates, which can further reduce the
runtime in certain cases. It may additionally lead to a framework for
optimizing circuit implementations over a gate set, reducing the overhead for
state-injection in fault-tolerant implementations. We provide a concise
exposition of randomized sparsification, and describe how to use it to estimate
circuit amplitudes in a way which can be generalized to a broader class of
gates and states. This latter method can be used to obtain additive error
estimates of circuit probabilities with a faster runtime than the full
techniques of Bravyi et al. Such estimates are useful for validating near-term
quantum devices provided that the target probability is not exponentially
small.
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quant-ph
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Many-body Chern number from statistical correlations of randomized
measurements: One of the main topological invariants that characterizes several
topologically-ordered phases is the many-body Chern number (MBCN). Paradigmatic
examples include several fractional quantum Hall phases, which are expected to
be realized in different atomic and photonic quantum platforms in the near
future. Experimental measurement and numerical computation of this invariant is
conventionally based on the linear-response techniques which require having
access to a family of states, as a function of an external parameter, which is
not suitable for many quantum simulators. Here, we propose an ancilla-free
experimental scheme for the measurement of this invariant, without requiring
any knowledge of the Hamiltonian. Specifically, we use the statistical
correlations of randomized measurements to infer the MBCN of a wavefunction.
Remarkably, our results apply to disk-like geometries that are more amenable to
current quantum simulator architectures.
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quant-ph
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The Uncertainty Relation for Smooth Entropies: Uncertainty relations give upper bounds on the accuracy by which the outcomes
of two incompatible measurements can be predicted. While established
uncertainty relations apply to cases where the predictions are based on purely
classical data (e.g., a description of the system's state before measurement),
an extended relation which remains valid in the presence of quantum information
has been proposed recently [Berta et al., Nat. Phys. 6, 659 (2010)]. Here, we
generalize this uncertainty relation to one formulated in terms of smooth
entropies. Since these entropies measure operational quantities such as
extractable secret key length, our uncertainty relation is of immediate
practical use. To illustrate this, we show that it directly implies security of
a family of quantum key distribution protocols including BB84. Our proof
remains valid even if the measurement devices used in the experiment deviate
arbitrarily from the theoretical model.
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quant-ph
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Coherence properties of photons emitted by single defect centers in
diamond: Photon interference among distant quantum emitters is a promising method to
generate large scale quantum networks. Interference is best achieved when
photons show long coherence times. For the nitrogen-vacancy defect center in
diamond we measure the coherence times of photons via optically induced Rabi
oscillations. Experiments reveal a close to Fourier transform (i.e. lifetime)
limited width of photons emitted even when averaged over minutes. The projected
contrast of two-photon interference (0.8) is high enough to envisage the
applications in quantum information processing. We report 12 and 7.8 ns excited
state lifetime depending on the spin state of the defect.
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quant-ph
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Quantum autoencoders for efficient compression of quantum data: Classical autoencoders are neural networks that can learn efficient low
dimensional representations of data in higher dimensional space. The task of an
autoencoder is, given an input $x$, is to map $x$ to a lower dimensional point
$y$ such that $x$ can likely be recovered from $y$. The structure of the
underlying autoencoder network can be chosen to represent the data on a smaller
dimension, effectively compressing the input. Inspired by this idea, we
introduce the model of a quantum autoencoder to perform similar tasks on
quantum data. The quantum autoencoder is trained to compress a particular
dataset of quantum states, where a classical compression algorithm cannot be
employed. The parameters of the quantum autoencoder are trained using classical
optimization algorithms. We show an example of a simple programmable circuit
that can be trained as an efficient autoencoder. We apply our model in the
context of quantum simulation to compress ground states of the Hubbard model
and molecular Hamiltonians.
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quant-ph
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Approaching single-photon pulses: Single-photon pulses cannot be generated on demand, due to incompatible
requirements of positive frequencies and positive times. Resulting states
therefore contain small probabilities for multiphotons. We derive upper and
lower bounds for the maximum fidelity of realizable states that approximate
single-photon pulses. The bounds have implications for ultrafast optics; the
maximum fidelity is low for pulses with few cycles or close to the onset, but
increases rapidly as the pulse envelope varies more slowly. We also demonstrate
strictly localized states that are close to single photons.
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quant-ph
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Investigating bound entangled two-qutrit states via the best separable
approximation: We use the linear programming algorithm introduced by Akulin et al. [V. M.
Akulin, G. A. Kabatiansky, and A. Mandilara, Phys. Rev. A 92, 042322 (2015)] to
perform best separable approximation on two-qutrit random density matrices. We
combine the numerical results with theoretical methods in order to generate
random representative families of positive partial transposed bound entangled
(BE) states and analyze their properties. Our results are disclosing that for
the two-qutrit system the BE states have negligible volume and that these form
tiny `islands' sporadically distributed over the surface of the polytope of
separable states. %We devise a method for estimating numerically the average
thickness of these formations and their frequency of occurrence. The detected
families of BE states are found to be located under a layer of pseudo one-copy
undistillable negative partial transposed states with the latter covering the
vast majority of the surface of the separable polytope.
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quant-ph
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A Non-existence Proof of Quantum Phase Transition in Spin-Boson Model: Quantum phase transition in the spin-boson model was claimed on the basis of
various numerical studies, but not strictly proven. Here by using a unitary
transformation to decompose the Hamiltonian into two branches of odd and even
parity we obtained the necessary and sufficient condition for degeneracy to
occur between states of opposite parity in the spin-boson model, and the
analytical expression for such degenerate energies. It can be strictly proven
that the ground state of spin-boson model with non-vanishing tunneling
amplitude must have an energy lower than the lowest possible such degenerate
energy, and have definite parity. Starting from the invariancy of the parity
operator we show that finite expansion by numerical calculation induces the
breaking of parity symmetry responsible for the phase transition. The critical
dissipation parameter we obtained for parity-symmetry breaking, as a
logarithmic function of summed diagonal matrix elements in the finite expansion
for the bosonic part of the parity operator, can reproduce the phase diagram
derived with quantum Monte Carlo method and logarithmically discretized
numberical renormalization group approach. It reveals that the quantum phase
transition in spin-boson model claimed by numerical procedures arises from
symmetry breaking caused by finite expansion in practical calculation. The
method we developed here may also be applicable to the discussion of quantum
chaos and other similar problems.
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quant-ph
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About the use of entanglement in the optical implementation of quantum
information processing: We review some applications of entanglement to improve quantum measurements
and communication, with the main focus on the optical implementation of quantum
information processing. The evolution of continuos variable entangled states in
active optical fibers is also analyzed.
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quant-ph
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Degree of Complementarity Determines the Nonlocality in Quantum
Mechanics: Complementarity principle is one of the central concepts in quantum mechanics
which restricts joint measurement for certain observables. Of course, later
development shows that joint measurement could be possible for such observables
with the introduction of a certain degree of unsharpness or fuzziness in the
measurement. In this paper, we show that the optimal degree of unsharpness,
which guarantees the joint measurement of all possible pairs of dichotomic
observables, determines the degree of nonlocality in quantum mechanics as well
as in more general no-signaling theories.
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quant-ph
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Linear-nonlinear duality for circuit design on quantum computing
platforms: The unitary description of beam splitters (BSs) and optical parametric
amplifiers (OPAs) in terms of the dynamical Lie groups $SU(2)$ and $SU(1,1)$
has a long history. Recently, an inherent duality has been proposed that
relates the unitaries of both optical devices. At the physical level, this
duality relates the linear nature of a lossless BS to the nonlinear Parametric
Down-Conversion (PDC) process exhibited by an OPA. Here, we argue that the
duality between BS and PDC can instead be naturally interpreted by analyzing
the geometrical properties of both Lie groups, an approach that explicitly
connects the dynamical group description of the optical devices with the
aforementioned duality. Furthermore, we show that the BS-PDC duality can be
represented through tensor network diagrams, enabling the implementation of a
PDC as a circuit on a standard quantum computing platform. Thus, it is feasible
to simulate nonlinear processes by using single-qubit unitaries that can be
implemented on currently available digital quantum processors.
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quant-ph
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Quasirandom quantum channels: Mixing (or quasirandom) properties of the natural transition matrix
associated to a graph can be quantified by its distance to the complete graph.
Different mixing properties correspond to different norms to measure this
distance. For dense graphs, two such properties known as spectral expansion and
uniformity were shown to be equivalent in seminal 1989 work of Chung, Graham
and Wilson. Recently, Conlon and Zhao extended this equivalence to the case of
sparse vertex transitive graphs using the famous Grothendieck inequality. Here
we generalize these results to the non-commutative, or `quantum', case, where a
transition matrix becomes a quantum channel. In particular, we show that for
irreducibly covariant quantum channels, expansion is equivalent to a natural
analog of uniformity for graphs, generalizing the result of Conlon and Zhao.
Moreover, we show that in these results, the non-commutative and commutative
(resp.) Grothendieck inequalities yield the best-possible constants.
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quant-ph
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Fundamental Limits on the Speed of Evolution of Quantum States: This paper reports on some new inequalities of
Margolus-Levitin-Mandelstam-Tamm-type involving the speed of quantum evolution
between two orthogonal pure states. The clear determinant of the qualitative
behavior of this time scale is the statistics of the energy spectrum. An
often-overlooked correspondence between the real-time behavior of a quantum
system and the statistical mechanics of a transformed (imaginary-time)
thermodynamic system appears promising as a source of qualitative insights into
the quantum dynamics.
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quant-ph
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Approximate quantum error correction, covariance symmetry, and their
relation: To perform reliable quantum computation, quantum error correction is
indispensable. In certain cases, continuous covariance symmetry of the physical
system can make exact error correction impossible. In this work we study the
approximate error correction and covariance symmetry from the
information-theoretic perspective. For general encoding and noise channels, we
define a quantity named infidelity to characterize the performance of the
approximate quantum error correction and quantify the noncovariance of an
encoding channel with respect to a general Lie group from the asymmetry measure
of the corresponding Choi state. In particular, when the encoding channel is
isometric, we derive a trade-off relation between infidelity and noncovariance.
Furthermore, we calculate the average infidelity and noncovariance measure for
a type of random code.
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quant-ph
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Thermal effect on mixed state geometric phases for neutrino propagation
in a magnetic field: In astrophysical environments, neutrinos may propagate over a long distance
in a magnetic field. In the presence of a rotating magentic field, the neutrino
spin can flip from left-handed neutrino to right-handed neutrino. Smirnov
demonstrated that the pure state geometric phase due to the neutrino spin
precession may cause resonantg spin conversion inside the Sun. However, in
general, the neutrinos may in an ensemble of thermal state. In this article,
the corresponding mixed state geometric phases will be formulated, including
the off-diagonal casse and diagonal ones. The spefic features towards
temperature will be analysized.
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quant-ph
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Simulating spin measurement with a finite heat bath model for the
environment: Spin measurement is studied as a unitary time evolution of the spin coupled
to an environment representing the meter and the apparatus. Modelling the
environment as a heat bath comprising only a finite number of boson modes and
represented in a basis of coherent states, following the Davydov ansatz, it can
be fully included in the quantum time evolution of the total system. We perform
numerical simulations of projective measurements of the polarization, with the
spins prepared initially in a neutral pure state. The likewise pure initial
state of the environment is constructed as a product of coherent states of the
boson modes with a random distribution of their centroids around the origin of
phase space. Switching the self-energy of the spin and the coupling to the heat
bath on and off by a time-dependent modulation, we observe the outcome of the
measurement in terms of the long-time behaviour of the spin. Interacting with
the heat bath, the spins get entangled with it and lose coherence, thus
reproduce the "collapse of the wavefunction". The expected quantum randomness
in the final state is manifest in our simulations as a tendency of the spin to
approach either one of the two eigenstates of the measured spin operator,
recovering an almost pure state. The unitary time evolution allows us to
reproducibly relate these random final states to the respective initial states
of the environment and to monitor the exchange of information between the two
subsystems in terms of their purity and mutual entropy.
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quant-ph
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Blind Quantum Computation without Trusted Center: Blind quantum computation (BQC) protocol allows a client having partially
quantum ability to del- egate his quantum computation to a remote quantum
server without leaking any information about the input, the output and the
intended computation. Recently, many BQC protocols have been proposed with the
intention to make the ability of client more classical. In this paper, we
propose two BQC protocols, in which the client does not have to generate
photons, but only has to perform either rotation or reorder on the received
photons.
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quant-ph
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Symplectic Radon Transform and the Metaplectic Representation: We study the symplectic Radon transform from the point of view of the
metaplectic representation of the symplectic group and its action on the
Lagrangian Grassmannian. We give rigorous proofs in the general setting of
multi-dimensional quantum systems. We interpret the inverse Radon transform as
a "demarginalization process" for the Wigner distribution. This work completes,
by giving complete proofs, a previous Note.
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quant-ph
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Mathematical Physics and Life: It is a fascinating subject to explore how well we can understand the
processes of life on the basis of fundamental laws of physics. It is emphasised
that viewing biological processes as manipulation of information extracts their
essential features. This information processing can be analysed using
well-known methods of computer science. The lowest level of biological
information processing, involving DNA and proteins, is the easiest one to link
to physical properties. Physical underpinnings of the genetic information that
could have led to the universal language of 4 nucleotide bases and 20 amino
acids are pointed out. Generalisations of Boolean logic, especially features of
quantum dynamics, play a crucial role.
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quant-ph
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Relativistic Treatment of the Hellmann-generalized Morse potential: We solve the relativistic equations(Klein-Gordon and Dirac equation) via the
conventional Nikiforov-Uvarov method. In order to overcome the centrifugal
barrier, we employed the well-known Greene and Aldrich approximation scheme.
The corresponding normalized eigenfunctions was also obtained in each case. It
was shown that in the non-relativistic limits, both energy equations obtained
by solving Klein-Gordon and Dirac equations, and wavefunctions reduced to the
non-relativisitc energy Equation. The bound state energy eigenvalues for N_2,
CO, NO, CH and HCl diatomic molecules were computed for various vibrational and
rotational quantum numbers. It was found that our results agree with those in
literature.
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Relativistic quantum coin tossing: A relativistic quantum information exchange protocol is proposed allowing two
distant users to realize ``coin tossing'' procedure. The protocol is based on
the point that in relativistic quantum theory reliable distinguishing between
the two orthogonal states generally requires a finite time depending on the
structure of these states.
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Cooperative light scattering in any dimension: We present a theory of cooperative light scattering valid in any dimension:
connecting theories for an open line, open plane, and open space in the
non-relativistic regime. This theory includes near-field and dipole-orientation
effects, highlighting how field mode confinement controls the phenomena. We
present a novel experimental implementation for planar collective effects.
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Time-efficient implementation of quantum search with qudits: We propose a simpler and more efficient scheme for the implementation of the
multi-valued Grover's quantum search. The multi-valued search generalizes the
original Grover's search by replacing qubits with qudits --- quantum systems of
$d$ discrete states. The qudit database is exponentially larger than the qubit
database and thus it requires fewer particles to control. The Hadamard gate,
which is the key elementary gate in the qubit implementation of Grover's
search, is replaced by a $d$-dimensional (complex-valued) unitary matrix $F$,
the only condition for which is to have a column of equal moduli elements
irrespective of their phases; it can be realized through any physical
interaction, which achieves an equal-weight superposition state. An example of
such a transformation is the $d$-dimensional discrete Fourier transform, used
in earlier proposals; however, its construction is much more costly than that
of the far simpler matrix $F$. We present examples of how such a transform $F$
can be constructed in realistic qudit systems in a \emph{single} interaction
step.
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Steady-State Two Atom Entanglement in a Pumped Cavity: In this paper we explore the possibility of a steady-state entanglement of
two two-level atoms inside a pumped cavity by taking into account cavity
leakage and the spontaneous emission of photons by the atoms. We describe the
system in the dressed state picture in which the coherence is built into the
dressed states while transitions between the dressed states are incoherent. Our
model assumes the vacuum Rabi splitting of the dressed states to be much larger
than any of the decay parameters of the system which allows atom-field
coherence to build up before any decay process takes over. We show that, under
our model, a pumping field cannot entangle two closed two-level atoms inside
the cavity in the steady-state, but a steady-state entanglement can be achieved
with two open two-level atoms.
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Particle Statistics in Quantum Information Processing: Particle statistics is a fundamental part of quantum physics, and yet its
role and use in the context of quantum information have been poorly explored so
far. After briefly introducing particle statistics and the Symmetrization
Postulate, I will argue that this fundamental aspect of Nature can be seen as a
resource for quantum information processing and I will present examples showing
how it is possible to do useful and efficient quantum information processing
using only the effects of particles statistics.
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Ultracold Fermions in a Graphene-Type Optical Lattice: Some important features of the graphene physics can be reproduced by loading
ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb
symmetry and we address here its experimental feasibility. We analyze in great
details the optical lattice generated by the coherent superposition of three
coplanar running laser waves with respective angles $2\pi/3$. The corresponding
band structure displays Dirac cones located at the corners of the Brillouin
zone and close to half-filling this system is well described by massless Dirac
fermions. We characterize their properties by accurately deriving the
nearest-neighbor hopping parameter $t_0$ as a function of the optical lattice
parameters. Our semi-classical instanton method proves in excellent agreement
with an exact numerical diagonalization of the full Hamilton operator in the
tight-binding regime. We conclude that the temperature range needed to access
the Dirac fermions regime is within experimental reach. We also analyze
imperfections in the laser configuration as they lead to optical lattice
distortions which affect the Dirac fermions. We show that the Dirac cones do
survive up to some critical intensity or angle mismatches which are easily
controlled in actual experiments. In the tight-binding regime, we predict, and
numerically confirm, that these critical mismatches are inversely proportional
to the square-root of the optical potential strength. We also briefly discuss
the interesting possibility of fine-tuning the mass of the Dirac fermions by
controlling the laser phase in an optical lattice generated by the incoherent
superposition of three coplanar independent standing waves with respective
angles $2\pi/3$.
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quant-ph
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Calculation of the Casimir Force between Similar and Dissimilar Metal
Plates at Finite Temperature: The Casimir pressure is calculated between parallel metal plates, containing
the materials Au, Cu, or Al. Our motivation for making this calculation is the
need of comparing theoretical predictions, based on the Lifshitz formula, with
experiments that are becoming gradually more accurate. In particular, the
finite temperature correction is considered, in view of the recent discussion
in the literature on this point. A special attention is given to the case where
the difference between the Casimir pressures at two different temperatures,
T=300 K and T=350 K, is involved. This seems to be a case that will be
experimentally attainable in the near future, and it will be a critical test of
the temperature correction.
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Fast Non-Adiabatic Two Qubit Gates for the Kane Quantum Computer: In this paper we apply the canonical decomposition of two qubit unitaries to
find pulse schemes to control the proposed Kane quantum computer. We explicitly
find pulse sequences for the CNOT, swap, square root of swap and controlled Z
rotations. We analyze the speed and fidelity of these gates, both of which
compare favorably to existing schemes. The pulse sequences presented in this
paper are theoretically faster, higher fidelity, and simpler than existing
schemes. Any two qubit gate may be easily found and implemented using similar
pulse sequences. Numerical simulation is used to verify the accuracy of each
pulse scheme.
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Superexponential behaviors of out-of-time ordered correlators and
Loschmidt echo in a non-Hermitian interacting system: We investigate, both analytically and numerically, the dynamics of quantum
chaos and quantum scrambling under many-body interaction effects via a
non-Hermitian Gross-Pitaevski map model, incorporating a periodically
modulated, complex strength of nonlinear interaction as delta kicks. We
establish a theoretical equivalence between a particular out-of-time ordered
correlator and the fidelity of a quantum state, which is proportional to the
Loschmidt echo. Both exhibit a double exponential growth in relation to time,
indicating the emergence of superexponential instability and
superexponentially-fast scrambling. The underlying mechanism is rooted in the
superexponentially-fast diffusion of energy, arising from the interplay between
the positive feedback of nonlinear interaction and the growth of the amplitude
of quantum state due to non-Hermiticity. Our findings suggest a kind of fastest
divergence of two nearby quantum states, which has implication in information
scrambling and brachistochrone evolution of quantum states.
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Is spacetime quantum?: Although the standard viewpoint in theoretical physics is that the
unification of quantum theory and general relativity requires the quantization
of gravity and spacetime, there is not consensus about whether spacetime must
fundamentally have any quantum features. Here we show a theorem stating that
spacetime degrees of freedom and a quantum system violate a Bell inequality in
a background Minkowski spacetime if a few properties of general relativity and
quantum theory have a broad range of validity, and if the quantum state
reduction upon measurement is a real physical process that is completed
superluminally when acting on distant quantum particles in a quantum entangled
state. We argue that this implies that spacetime cannot be sensibly called
classical if the assumptions in our theorem hold. In contrast to the
Eppley-Hannah argument for the necessity of quantizing the gravitational field,
we discuss the validity of our assumptions, our thought experiment does not
require to manipulate or detect gravitational waves, and our theorem does not
rely on the conservation of momentum or on the uncertainty principle.
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Unsupervised phase discovery with deep anomaly detection: We demonstrate how to explore phase diagrams with automated and unsupervised
machine learning to find regions of interest for possible new phases. In
contrast to supervised learning, where data is classified using predetermined
labels, we here perform anomaly detection, where the task is to differentiate a
normal data set, composed of one or several classes, from anomalous data. Asa
paradigmatic example, we explore the phase diagram of the extended Bose Hubbard
model in one dimension at exact integer filling and employ deep neural networks
to determine the entire phase diagram in a completely unsupervised and
automated fashion. As input data for learning, we first use the entanglement
spectra and central tensors derived from tensor-networks algorithms for
ground-state computation and later we extend our method and use experimentally
accessible data such as low-order correlation functions as inputs. Our method
allows us to reveal a phase-separated region between supersolid and superfluid
parts with unexpected properties, which appears in the system in addition to
the standard superfluid, Mott insulator, Haldane-insulating, and density wave
phases.
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Entanglement and Quantum phase transition in topological insulators: Presence of entangled states is explicitly shown in Topological insulator
(TI) $Bi_2Te_3$. The surface and bulk state are found to have the different
structures of entanglement. The surface states live as maximally entangled
states in the four-dimensional subspace of total Hilbert space (spin, orbital,
space). However, bulk states are entangled in the whole Hilbert space. Bulk
states are found to be entangled maximally by controlled injection of electrons
with momentum only along the z-direction. Scheme to detect entanglement in a
2-D model using measurement, confirming natural implementation of universal
Hadamard with Controlled-NOT gates is explicated.
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Generating higher order quantum dissipation from lower order parametric
processes: Stabilization of quantum manifolds is at the heart of error-protected quantum
information storage and manipulation. Nonlinear driven-dissipative processes
achieve such stabilization in a hardware efficient manner. Josephson circuits
with parametric pump drives implement these nonlinear interactions. In this
article, we propose a scheme to engineer a four-photon drive and dissipation on
a harmonic oscillator by cascading experimentally demonstrated two-photon
processes. This would stabilize a four-dimensional degenerate manifold in a
superconducting resonator. We analyze the performance of the scheme using
numerical simulations of a realizable system with experimentally achievable
parameters.
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Bell's theorem: Critique of proofs with and without inequalities: Most of the standard proofs of the Bell theorem are based on the Kolmogorov
axioms of probability theory. We show that these proofs contain mathematical
steps that cannot be reconciled with the Kolmogorov axioms. Specifically we
demonstrate that these proofs ignore the conclusion of a theorem of Vorob'ev on
the consistency of joint distributions. As a consequence Bell's theorem stated
in its full generality remains unproven, in particular, for extended parameter
spaces that are still objective local and that include instrument parameters
that are correlated by both time and instrument settings. Although the Bell
theorem correctly rules out certain small classes of hidden variables, for
these extended parameter spaces the standard proofs come to a halt. The
Greenberger-Horne-Zeilinger (GHZ) approach is based on similar fallacious
arguments. For this case we are able to present an objective local computer
experiment that simulates the experimental test of GHZ performed by Pan,
Bouwmeester, Daniell, Weinfurter and Zeilinger and that directly contradicts
their claim that Einstein-local elements of reality can neither explain the
results of quantum mechanical theory nor their experimental results.
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A Quantum Structure Description of the Liar Paradox: In this article we propose an approach that models the truth behavior of
cognitive entities (i.e. sets of connected propositions) by taking into account
in a very explicit way the possible influence of the cognitive person (the one
that interacts with the considered cognitive entity). Hereby we specifically
apply the mathematical formalism of quantum mechanics because of the fact that
this formalism allows the description of real contextual influences, i.e. the
influence of the measuring apparatus on the physical entity. We concentrated on
the typical situation of the liar paradox and have shown that (1) the
truth-false state of this liar paradox can be represented by a quantum vector
of the non-product type in a finite dimensional complex Hilbert space and the
different cognitive interactions by the actions of the corresponding quantum
projections, (2) the typical oscillations between false and truth - the paradox
-is now quantum dynamically described by a Schrodinger equation. We analyse
possible philosophical implications of this result.
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quant-ph
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Dicke States Generation via Selective Interactions in Dicke-Stark Model: We propose a method to create selective interactions with Dicke-Stark model
by means of time-dependent perturbation theory. By choosing the proper rotating
framework, we find that the time oscillating terms depend on the number of
atomic excitations and the number of photonic excitations. Consequently, the
Rabi oscillation between selective states can be realized by properly choosing
the frequency of the two-level system. The second order selective interactions
can also be studied with this method. Then various states such as Dicke states,
superposition of Dicke states and GHZ states can be created by means of such
selective interactions. The numerical results show that high fidelity Dicke
states and Greenberger-Horne-Zeilinger states can be created by choosing the
proper frequency of two-level system and controlling the evolution time.
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quant-ph
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PCOAST: A Pauli-based Quantum Circuit Optimization Framework: This paper presents the Pauli-based Circuit Optimization, Analysis, and
Synthesis Toolchain (PCOAST), a framework for quantum circuit optimizations
based on the commutative properties of Pauli strings. Prior work has
demonstrated that commuting Clifford gates past Pauli rotations can expose
opportunities for optimization in unitary circuits. PCOAST extends that
approach by adapting the technique to mixed unitary and non-unitary circuits
via generalized preparation and measurement nodes parameterized by Pauli
strings. The result is the PCOAST graph, which enables novel optimizations
based on whether a user needs to preserve the quantum state after executing the
circuit, or whether they only need to preserve the measurement outcomes.
Finally, the framework adapts a highly tunable greedy synthesis algorithm to
implement the PCOAST graph with a given gate set.
PCOAST is implemented as a set of compiler passes in the Intel Quantum SDK.
In this paper, we evaluate its compilation performance against two leading
quantum compilers, Qiskit and tket. We find that PCOAST reduces total gate
count by 32.53% and 43.33% on average, compared to to the best performance
achieved by Qiskit and tket respectively, two-qubit gates by 29.22% and 20.58%,
and circuit depth by 42.02% and 51.27%.
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Entanglement polygon inequality in qudit systems: Entanglement is one of important resources for quantum communication tasks.
Most of results are focused on qubit entanglement. Our goal in this work is to
characterize the multipartite high-dimensional entanglement. We firstly derive
an entanglement polygon inequality for the $q$-concurrence, which manifests the
relationship among all the "one-to-group" marginal entanglements in any
multipartite qudit system. This implies lower and upper bounds for the marginal
entanglement of any three-qudit system. We further extend to general
entanglement distribution inequalities for high-dimensional entanglement in
terms of the unified-$(r, s)$ entropy entanglement including Tsallis entropy,
R\'{e}nyi entropy, and von Neumann entropy entanglement as special cases. These
results provide new insights into characterizing bipartite high-dimensional
entanglement in quantum information processing.
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Quantum Information Processing using coherent states in cavity QED: Using the highly detuned interaction between three-level $\Lambda$-type atoms
and coherent optical fields, we can realize the C-NOT gates from atoms to
atoms, optical fields to optical fields, atoms to optical fields and optical
fields to atoms. Based on the realization of the C-NOT gates we propose an
entanglement purification scheme to purify a mixed entangled states of coherent
optical fields. The simplicity of the current scheme makes it possible that it
will be implemented in experiment in the near future.
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quant-ph
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Ground State Microwave-Stimulated Raman Transitions and Adiabatic Spin
Transfer in the $^{15}$Nitrogen-Vacancy Center: Microwave pulse sequences are the basis of coherent manipulation of the
electronic spin ground state in nitrogen-vacancy (NV) centers. In this work we
demonstrate stimulated Raman transitions (SRT) and stimulated Raman adiabatic
passage (STIRAP), two ways to drive the dipole-forbidden transition between two
spin sublevels in the electronic triplet ground state of the NV center. This is
achieved by a multitone Raman microwave pulse which simultaneously drives two
detuned transitions via a virtual level for SRT or via two adiabatic and
partially overlapping resonant microwave pulses for STIRAP. We lay the
theoretical framework of SRT and STIRAP dynamics and verify experimentally the
theoretical predictions of population inversion by observing the
dipole-forbidden transition in the ground state of a single NV center. A
comparison of the two schemes showed a better robustness and success of the
spin swap for STIRAP as compared to SRT.
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The Central Mystery of Quantum Mechanics: A critical re-examination of the double-slit experiment and its variants is
presented to clarify the nature of what Feynmann called the ``central mystery''
and the ``only mystery'' of quantum mechanics, leading to an interpretation of
complementarity in which a `wave {\em and} particle' description rather than a
`wave {\em or} particle' description is valid for the {\em same} experimental
set up, with the wave culminating in the particle sequentially in time. This
interpretation is different from Bohr's but is consistent with the von Neumann
formulation as well as some more recent interpretations of quantum mechanics.
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quant-ph
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Work and efficiency fluctuations in a quantum Otto cycle with idle
levels: We study the performance of a quantum Otto heat engine with two spins coupled
by a Heisenberg interaction, taking into account not only the mean values of
work and efficiency but also their fluctuations. We first show that, for this
system, the output work and its fluctuations are directly related to the
magnetization and magnetic susceptibility of the system at equilibrium with
either heat bath. We analyze the regions where the work extraction can be done
with low relative fluctuation for a given range of temperatures, while still
achieving an efficiency higher than that of a single spin system heat engine.
In particular, we find that, due to the presence of `idle' levels, an increase
in the inter-spin coupling can either increase or decrease fluctuations,
depending on the other parameters. In all cases, however, we find that the
relative fluctuations in work or efficiency remain large, implying that this
microscopic engine is not very reliable as a source of work.
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quant-ph
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Coherent competition and control between three-wave mixing and four-wave
mixing in superconducting circuits: Exploring intermixing and interplay between different frequency-mixing
processes has always been one of the interesting subjects at the interface of
nonlinear optics with quantum optics. Here we investigate coherent competition
and control between three-wave mixing (TWM) and four-wave mixing (FWM) in a
cyclic three-level superconducting quantum system. In the weak control-field
regime, strong competition leads to an alternating oscillation between TWM and
FWM signals and this oscillation is a signature of strong energy exchange
between these two nonlinear processes. In particular, such oscillation is
absent from conventional multi-wave mixing in atomic systems. Surprisingly,
synchronous TWM and FWM processes are demonstrated in the strong control-field
regime and, at the same time, their efficiencies can be as high as 40% and 45%,
respectively. Our study shows that these competitive behaviors between TWM and
FWM can be manipulated by tuning the control-field intensity.
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Quantum thermal waves in quantum corrals: In this paper the possibility of the generation of the thermal waves in 2D
electron gas is investigated. In the frame of the quantum heat transport theory
the 2D quantum hyperbolic heat transfer equation is formulated and numerically
solved. The obtained solutions are the thermal waves in electron 2D gases. As
an exapmle the thermal waves in quantum corrals are described.
Key words: 2D electron gas, quantum corrals, thermal waves.
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quant-ph
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Simplified Hartree-Fock Computations on Second-Row Atoms: Simplified Hartree-Fock computations are carried out on the atoms He through
Ne, using orthonormalized basis functions for the 1s, 2s and 2p orbitals
dependent on three parameters. Using Mathematica with the new Apple M1 chip,
computations require about 0.005 seconds of CPU time. Approximate energies
within 1% of the best H-F values are thereby obtained, with an order of
magnitude less computational effort.
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quant-ph
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Singularities of Floquet Scattering and Tunneling: We study quasi-bound states and scattering with short range potentials in
three dimensions, subject to an axial periodic driving. We find that poles of
the scattering S-matrix can cross the real energy axis as a function of the
drive amplitude, making the S-matrix nonanalytic at a singular point. For the
corresponding quasi-bound states that can tunnel out of (or get captured
within) a potential well, this results in a discontinuous jump in both the
angular momentum and energy of emitted (absorbed) waves. We also analyze
elastic and inelastic scattering of slow particles in the time dependent
potential. For a drive amplitude at the singular point, there is a total
absorption of incoming low energy (s-wave) particles and their conversion to
high energy outgoing (mostly p-) waves. We examine the relation of such Floquet
singularities, lacking in an effective time independent approximation, with
well known "spectral singularities" (or "exceptional points"). These results
are based on an analytic approach for obtaining eigensolutions of
time-dependent periodic Hamiltonians with mixed cylindrical and spherical
symmetry, and apply broadly to particles interacting via power law forces and
subject to periodic fields, e.g. co-trapped ions and atoms.
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Design Automation and Design Space Exploration for Quantum Computers: A major hurdle to the deployment of quantum linear systems algorithms and
recent quantum simulation algorithms lies in the difficulty to find inexpensive
reversible circuits for arithmetic using existing hand coded methods. Motivated
by recent advances in reversible logic synthesis, we synthesize arithmetic
circuits using classical design automation flows and tools. The combination of
classical and reversible logic synthesis enables the automatic design of large
components in reversible logic starting from well-known hardware description
languages such as Verilog. As a prototype example for our approach we
automatically generate high quality networks for the reciprocal $1/x$, which is
necessary for quantum linear systems algorithms.
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quant-ph
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Markovianization with approximate unitary designs: Memoryless processes are ubiquitous in nature, in contrast with the
mathematics of open systems theory, which states that non-Markovian processes
should be the norm. This discrepancy is usually addressed by subjectively
making the environment forgetful. Here we prove that there are physical
non-Markovian processes that with high probability look highly Markovian for
all orders of correlations; we call this phenomenon Markovianization. Formally,
we show that when a quantum process has dynamics given by an approximate
unitary design, a large deviation bound on the size of non-Markovian memory is
implied. We exemplify our result employing an efficient construction of an
approximate unitary circuit design using two-qubit interactions only, showing
how seemingly simple systems can speedily become forgetful. Conversely, since
the process is closed, it should be possible to detect the underlying
non-Markovian effects. However, for these processes, observing non-Markovian
signatures would require highly entangling resources and hence be a difficult
task.
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Geometric phase and quantum potential: We show that the geometric phase of Levy-Leblond arises from a low of
parallel transport for wave functions and point out that this phase belongs to
a new class of geometric phases due to the presence of a quantum potential.
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quant-ph
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OAM tomography with Heisenberg-Weyl observables: Photons carrying orbital angular momentum (OAM) are excellent qudits and are
widely used in several applications, such as long distance quantum
communication, $d$-dimensional teleportation and high-resolution imaging and
metrology. All these protocols rely on quantum tomography to characterise the
OAM state, which currently requires complex measurements involving spatial
light modulators and mode filters. To simplify the measurement and
characterisation of OAM states, here we apply a recent tomography protocol
[Asadian et al., \pra {\bf 94}, 010301 (2016)]. Our scheme for OAM tomography
in $d$ dimensions requires only a set of measurements on a mode qubit, i.e., a
2-dimensional system. This replaces the current complexity of OAM measurements
by the ability to perform generalized Pauli operators $X_d, Z_d$ on OAM states.
Our scheme can be adapted in principle to other degrees of freedom, thus
opening the way for more complex qudit tomography.
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quant-ph
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Fisher information analysis on post-selection involved quantum precision
measurements using optical coherent states: The weak-value-amplification (WVA) technique has been extensively considered
and debated in the field of quantum precision measurement, largely owing to the
reduced Fisher information caused by the low probability of successful
post-selection. %% In this work we show that, rather than the Gaussian meter
state as typically considered, using the optical coherent state as a meter, the
WVA measurement can definitely outperform the conventional measurement not
involving the strategy of post-selection. %% We also show that the
post-selection procedure involved in the WVA scheme can make a mixture of
coherent states work better than a pure coherent state with identical average
photon numbers. This is in sharp contrast to the claim proved in the absence of
post-selection. The post-selection strategy can also result in the precision of
Heisenberg (or even "super-Heisenberg") scaling with the photon numbers, but
without using any expensive quantum resources. %% The present work may
stimulate further investigations for the potential of the post-selection
strategy in quantum precision measurements.
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Quantum Walks of Two Interacting Particles in One Dimension: We investigate continuous-time quantum walks of two indistinguishable
particles (bosons, fermions or hard-core bosons) in one-dimensional lattices
with nearest-neighbour interactions. The two interacting particles can undergo
independent- and/or co-walking dependent on both quantum statistics and
interaction strength. We find that two strongly interacting particles may form
a bound state and then co-walk like a single composite particle with
statistics-dependent propagation speed. Such an effective single-particle
picture of co-walking is analytically derived in the context of degenerate
perturbation and the analytical results are well consistent with direct
numerical simulation. In addition to implementing universal quantum computation
and observing bound states, two-particle quantum walks offer a novel route to
detecting quantum statistics. Our theoretical results can be examined in
experiments of light propagations in two-dimensional waveguide arrays or
spin-impurity dynamics of ultracold atoms in one-dimensional optical lattices.
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quant-ph
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Dynamical decoupling with tailored waveplates for long distance
communication using polarization qubits: We address the issue of dephasing effects in flying polarization qubits
propagating through optical fiber by using the method of dynamical decoupling.
The control pulses are implemented with half waveplates suitably placed along
the realistic lengths of the single mode optical fiber. The effects of the
finite widths of the waveplates on the polarization rotation are modeled using
tailored refractive index profiles inside the waveplates. We show that
dynamical decoupling is effective in preserving the input qubit state with the
fidelity close to one when the polarization qubit is subject to the random
birefringent noise in the fiber, as well the rotational imperfections
(flip-angle errors) due to the finite width of the waveplates.
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quant-ph
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Imaging the interface of a qubit and its quantum-many-body environment: Decoherence affects all quantum systems, natural or artificial, and is the
primary obstacle impeding quantum technologies. We show theoretically that for
a Rydberg qubit in a Bose condensed environment, experiments can image the
system-environment interface that is central for decoherence. High precision
absorption images of the condensed environment will be able to capture
transient signals that show the real time build up of a mesoscopic entangled
state in the environment. This is possible before decoherence sources other
than the condensate itself can kick in, since qubit decoherence time-scales can
be tuned from the order of nanoseconds to microseconds by choice of the excited
Rydberg principal quantum number {\nu}. Imaging the interface will allow
detailed explorations of open quantum system concepts and may offer guidance
for coherence protection in challenging scenarios with non-Markovian
environments.
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quant-ph
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Focus on topological quantum computation: Topological quantum computation started as a niche area of research aimed at
employing particles with exotic statistics, called anyons, for performing
quantum computation. Soon it evolved to include a wide variety of disciplines.
Advances in the understanding of anyon properties inspired new quantum
algorithms and helped in the characterisation of topological phases of matter
and their experimental realisation. The conceptual appeal of topological
systems as well as their promise for building fault-tolerant quantum
technologies fuelled the fascination in this field. This `focus on' brings
together several of the latest developments in the field and facilitates the
synergy between different approaches.
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quant-ph
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Quantum Nature of Light Measured With a Single Detector: We realized the most fundamental quantum optical experiment to prove the
non-classical character of light: Only a single quantum emitter and a single
superconducting nanowire detector were used. A particular appeal of our
experiment is its elegance and simplicity. Yet its results unambiguously
enforce a quantum theory for light. Previous experiments relied on more complex
setups, such as the Hanbury-Brown-Twiss configuration, where a beam splitter
directs light to two photodetectors, giving the false impression that the beam
splitter is required. Our work results in a major simplification of the widely
used photon-correlation techniques with applications ranging from quantum
information processing to single-molecule detection.
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quant-ph
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Sub-Poissonian atom number fluctuations using light-assisted collisions: We investigate experimentally the number statistics of a mesoscopic ensemble
of cold atoms in a microscopic dipole trap loaded from a magneto-optical trap,
and find that the atom number fluctuations are reduced with respect to a
Poisson distribution due to light-assisted two-body collisions. For numbers of
atoms N>2, we measure a reduction factor (Fano factor) of 0.72+/-0.07, which
differs from 1 by more than 4 standard deviations. We analyze this fact by a
general stochastic model describing the competition between the loading of the
trap from a reservoir of cold atoms and multi-atom losses, which leads to a
master equation. Applied to our experimental regime, this model indicates an
asymptotic value of 3/4 for the Fano factor at large N and in steady state. We
thus show that we have reached the ultimate level of reduction in number
fluctuations in our system.
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quant-ph
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Device-dependent and device-independent quantum key distribution without
a shared reference frame: Standard quantum key distribution (QKD) protocols typically assume that the
distant parties share a common reference frame. In practice, however,
establishing and maintaining a good alignment between distant observers is
rarely a trivial issue, which may significantly restrain the implementation of
long-distance quantum communication protocols. Here we propose simple QKD
protocols that do not require the parties to share any reference frame, and
study their security and feasibility in both the usual device-dependent
case--in which the two parties use well characterized measurement devices--as
well as in the device-independent case--in which the measurement devices can be
untrusted, and the security relies on the violation of a Bell inequality. To
illustrate the practical relevance of these ideas, we present a
proof-of-principle demonstration of our protocols using polarization entangled
photons distributed over a coiled 10-km-long optical fiber. We consider two
situations, in which either the fiber spool freely drifts, or randomly chosen
polarization transformations are applied. The correlations obtained from
measurements allow, with high probability, to generate positive asymptotic
secret key rates in both the device-dependent and device-independent scenarios
(under the fair-sampling assumption for the latter case).
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quant-ph
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Decoherence and entanglement degradation of a qubit-qutrit system in
non-inertial frames: We study the effect of decoherence on a qubit-qutrit system under the
influence of global, local and multilocal decoherence in non-inertial frames.
We show that the entanglement sudden death can be avoided in non-inertial
frames in the presence of amplitude damping, depolarizing and phase damping
channels. However, degradation of entanglement is seen due to Unruh effect. It
is shown that for lower level of decoherence, the depolarizing channel degrades
the entanglement more heavily as compared to the amplitude damping and phase
damping channels. However, for higher values of decoherence parameters,
amplitude damping channel heavily degrades the entanglement of the hybrid
system. Further more, no ESD is seen for any value of Rob's acceleration.
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quant-ph
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A hybrid quantum eraser scheme for characterization of free-space and
fiber communication channels: We demonstrate a simple projective measurement based on the quantum eraser
concept that can be used to characterize the disturbances of any communication
channel. Quantum erasers are commonly implemented as spatially separated path
interferometric schemes. Here we exploit the advantages of redefining the
which-path information in terms of spatial modes, replacing physical paths with
abstract paths of orbital angular momentum (OAM). Remarkably, vector modes
(natural modes of free-space and fiber) have a non-separable feature of
spin-orbit coupled states, equivalent to the description of two independently
marked paths. We explore the effects of fiber perturbations by probing a
step-index optical fiber channel with a vector mode, relevant to high-order
spatial mode encoding of information for ultra-fast fiber communications.
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quant-ph
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Optimal fermionic swap networks for Hubbard models: We propose an efficient variation of the fermionic swap network scheme used
to efficiently simulate n-dimensional Fermi-Hubbard-model Hamiltonians encoded
using the Jordan-Wigner transform. For the two-dimensional versions, we show
that our choices minimize swap depth and number of Hamiltonian interaction
layers. The proofs, along with the choice of swap network, rely on
isoperimetric inequality results from the combinatorics literature, and are
closely related to graph bandwidth problems. The machinery has the potential to
be extended to maximize swap network efficiency for other types of lattices.
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quant-ph
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Towards experimental tests and applications of Lieb-Robinson bounds: Spin-polarized scanning tunneling microscopy is identified as a suitable
experimental technique to investigate the quantitative quality of Lieb-Robinson
bounds on the signal velocity. The latest, most general bound is simplified and
it is shown that there is a discrepancy by a factor of approximately 4 between
the corresponding limit speed and some estimated exact velocities in atomic
spin chains. The observed discrepancy facilitates conclusions for a further
mathematical improvement of Lieb-Robinson bounds. The real signal propagation
can be modified with several experimental parameters from which the bounds are
independent. This enables the application of Lieb-Robinson bounds as upper
limits on the enhancement of the real signal speed for information transport in
spintronic devices.
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quant-ph
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Quantum control limited by quantum decoherence: We describe quantum controllability under the influences of the quantum
decoherence induced by the quantum control itself. It is shown that, when the
controller is considered as a quantum system, it will entangle with its
controlled system and then cause quantum decoherence in the controlled system.
In competition with this induced decoherence, the controllability will be
limited by some uncertainty relation in a well-armed quantum control process.
In association with the phase uncertainty and the standard quantum limit, a
general model is studied to demonstrate the possibility of realizing a
decoherence-free quantum control with a finite energy within a finite time. It
is also shown that if the operations of quantum control are to be determined by
the initial state of the controller, then due to the decoherence which results
from the quantum control itself, there exists a low bound for quantum
controllability.
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quant-ph
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Security analysis of decoy state quantum key distribution incorporating
finite statistics: Decoy state method quantum key distribution (QKD) is one of the promising
practical solutions to BB84 QKD with coherent light pulses. In the real world,
however, statistical fluctuations with the finite code length cannot be
negligible, and the securities of theoretical and experimental researches of
the decoy method state QKD so far are based on the asymptotic GLLP's formula
which guarantees only that the limit of eavesdropper's information becomes zero
as the code length approaches infinity. In this paper, we propose a
substantially improved decoy state QKD in the framework of the finite code
length and derive the upper bound of eavesdropper's information in the finite
code length decoy state QKD with arbitrary number of decoy states of different
intensities incorporating the finite statistics. We also show the performance
of our decoy QKD and optimal values of parameters by numerical simulation.
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quant-ph
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An exact solution to the Dirac equation for a time dependent Hamiltonian
in 1-1D space-time: We find an exact solution to the Dirac equation in 1-1 dimensional space-time
in the presence of a time-dependent potential which consists of a combination
of electric, scalar, and pseudoscalar terms.
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quant-ph
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Dirac systems with magnetic field and position dependent mass: Darboux
transformations and equivalence with generalized Dirac oscillators: We construct a Darboux transformation for a class of two-dimensional Dirac
systems at zero energy. Our starting equation features a position-dependent
mass, a matrix potential, and an additional degree of freedom that can be
interpreted either as a magnetic field perpendicular to the plane or a
generalized Dirac oscillator interaction. We obtain a number of
Darbouxtransformed Dirac equations for which the zero energy solutions are
exactly known.
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quant-ph
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Single-ancilla ground state preparation via Lindbladians: We design a quantum algorithm for ground state preparation in the early fault
tolerant regime. As a Monte Carlo-style quantum algorithm, our method features
a Lindbladian where the target state is stationary, and its evolution can be
efficiently implemented using just one ancilla qubit. Our algorithm can prepare
the ground state even when the initial state has zero overlap with the ground
state, bypassing the most significant limitation of methods like quantum phase
estimation. As a variant, we also propose a discrete-time algorithm,
demonstrating even better efficiency and providing a near-optimal simulation
cost depending on the desired evolution time and precision. Numerical
simulation using Ising models and Hubbard models demonstrates the efficacy and
applicability of our method.
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quant-ph
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Magnetic pseudo-fields in a rotating electron-nuclear spin system: A precessing spin observed in a rotating frame of reference appears
frequency-shifted, an effect analogous to the precession of a Foucault pendulum
observed on the rotating Earth. This frequency shift can be understood as
arising from a magnetic pseudo-field in the rotating frame that nevertheless
has physically significant consequences, such as the Barnett effect. Detecting
these pseudo-fields is experimentally challenging, as a rotating-frame sensor
is required. Previous work has realised classical rotating-frame detectors.
Here we use quantum sensors, nitrogen-vacancy (NV) centres, in a rapidly
rotating diamond to detect pseudo-fields in the rotating frame. While
conventional magnetic fields induce precession at a rate proportional to the
gyromagnetic ratio, rotation shifts the precession of all spins equally, and
thus primarily affect nearby $^{13}$C nuclear spins. We are thus able to
explore these effects via quantum sensing in a rapidly rotating frame, and
define a new approach to quantum control using rotationally-induced nuclear
spin-selective magnetic fields. This work provides an integral step towards
realising precision rotation sensing and quantum spin gyroscopes.
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quant-ph
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Generation of discord through a remote joint continuous variable
measurement: In quantum mechanics, continuously measuring an observable steers the system
into one eigenstate of that observable. This property has interesting and
useful consequences when the observable is a joint property of two remotely
separated qubits. In particular, if the measurement of the two-qubit joint
observable is performed in a way that is blind to single-qubit information,
quantum back-action generates correlation of the discord type even if the
measurement is weak and inefficient. We demonstrate the ability to generate
these quantum correlations in a circuit-QED setup by performing a weak joint
readout of two remote, non-interacting, superconducting transmon qubits using
the two non-degenerate modes of a Josephson Parametric Converter (JPC).
Single-qubit information is erased from the output in the limit of large gain
and with properly tailored cavity drive pulses. Our results of the measurement
of discord are in quantitative agreement with theoretical predictions, and
demonstrate the utility of the JPC as a which-qubit information eraser.
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quant-ph
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Relativistic Tunneling Through Two Successive Barriers: We study the relativistic quantum mechanical problem of a Dirac particle
tunneling through two successive electrostatic barriers. Our aim is to study
the emergence of the so-called \emph{Generalized Hartman Effect}, an effect
observed in the context of nonrelativistic tunneling as well as in its
electromagnetic counterparts, and which is often associated with the
possibility of superluminal velocities in the tunneling process. We discuss the
behavior of both the phase (or group) tunneling time and the dwell time, and
show that in the limit of opaque barriers the relativistic theory also allows
the emergence of the Generalized Hartman Effect. We compare our results with
the nonrelativistic ones and discuss their interpretation.
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quant-ph
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Quantum annealing of the $p$-spin model under inhomogeneous transverse
field driving: We solve the mean-field-like $p$-spin Ising model under a spatio-temporal
inhomogeneous transverse field to study the effects of inhomogeneity on the
performance of quantum annealing. We find that the problematic first-order
quantum phase transition that arises under the conventional homogeneous field
protocol can be avoided if the temperature is zero and the local field is
completely turned off site by site after a finite time. When these ideal
conditions are not satisfied, a new series of first-order transitions appear,
which prevents us from driving the system while avoiding first-order
transitions. Nevertheless, under these non-ideal conditions, quantitative
improvements can be obtained in terms of narrower tunneling barriers in the
free energy landscape. A comparison with classical simulated annealing
establishes a limited quantum advantage in the ideal case, since inhomogeneous
temperature driving in simulated annealing cannot remove a first-order
transition, in contrast to the quantum case. The classical model of spin-vector
Monte Carlo is also analyzed, and we find it to have the same thermodynamic
phase diagram as the quantum model in the ideal case, with deviations arising
at non-zero temperature.
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quant-ph
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Comment on a suggested Kochen-Specker test: A suggestion for an observational test of the difference between quantum
mechanics and noncontextual hidden variables theories requires the measurement
of a product of two commuting observables without measuring either observable
separately. A proposal has been made for doing this, but it is shown to be
problematic.
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quant-ph
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Local randomness in Hardy's correlations: Implications from information
causality principle: Study of nonlocal correlations in term of Hardy's argument has been quite
popular in quantum mechanics. Recently Hardy's argument of non-locality has
been studied in the context of generalized non-signaling theory as well as
theory respecting information causality. Information causality condition
significantly reduces the success probability for Hardy's argument when
compared to the result based on non-signaling condition. Here motivated by the
fact that maximally entangled state in quantum mechanics does not exhibit
Hardy's non-local correlation, we do a qualitative study of the property of
local randomness of measured observable on each side reproducing Hardy's
non-locality correlation,in the context of information causality condition. On
applying the necessary condition for respecting the principle of information
causality, we find that there are severe restrictions on the local randomness
of measured observable in contrast to results obtained from no-signaling
condition.Still, there are some restrictions imposed by quantum mechanics that
are not obtained from information causality condition.
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quant-ph
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Ruling out the class of statistical processes involving two
noninteracting identical particles in two modes: In the framework of Generalized probabilistic theories (GPT), we illustrate a
class of statistical processes in case of two noninteracting identical
particles in two modes that satisfies a well motivated notion of physicality
conditions namely the double stochasticity and the no-interaction condition
proposed by Karczewski et. al. (Phys. Rev. Lett. 120, 080401 (2018)), which can
not be realized through a quantum mechanical process. This class of statistical
process is ruled out by an additional requirement called the evolution
condition imposed on two particle evolution. We also show that any statistical
process of two noninteracting identical particles in two modes that satisfies
all of the three physicality conditions can be realized within quantum
mechanics using the beam splitter operation.
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quant-ph
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Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum
Gates\\ with Optimal Control in a Trapped Ion: Quantum computation with quantum gates induced by geometric phases is
regarded as a promising strategy in fault tolerant quantum computation, due to
its robustness against operational noises. However, because of the parametric
restriction of previous schemes, the main robust advantage of holonomic quantum
gates is smeared. Here, we experimentally demonstrate a solution scheme,
demonstrating nonadiabatic holonomic single qubit quantum gates with optimal
control in a trapped Yb ion based on three level systems with resonant drives,
which also hold the advantages of fast evolution and convenient implementation.
Compared with corresponding previous geometric gates and conventional dynamic
gates, the superiority of our scheme is that it is more robust against control
amplitude errors, which is confirmed by the measured gate infidelity through
both quantum process tomography and random benchmarking methods. In addition,
we also outline that nontrivial two qubit holonomic gates can also be realized
within current experimental technologies. Therefore, our experiment validates
the feasibility for this robust and fast holonomic quantum computation
strategy.
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quant-ph
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Quantum Statistics of Identical Particles: The empirical rule that systems of identical particles always obey either
Bose or Fermi statistics is customarily imposed on the theory by adding it to
the axioms of nonrelativistic quantum mechanics, with the result that other
statistical behaviors are excluded a priori. A more general approach is to ask
what other many-particle statistics are consistent with the
indistinguishability of identical particles. This strategy offers a way to
discuss possible violations of the Pauli Exclusion Principle, and it leads to
some interesting issues related to preparation of states and a superselection
rule arising from invariance under the permutation group.
|
quant-ph
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Can Traditional Terrestrial Applications of Gravity Gradiometry Rely
Upon Quantum Technologies ? A Side View: The era of practical terrestrial applications of gravity gradiometry begun in
1890 when Baron Lorand von E\"otv\"os, a Hungarian nobleman and a talented
physicist and engineer, invented his famous torsion balance - the first
practical gravity gradients measuring device. It was credited for the major oil
discoveries later in Texas (USA). A 100 years later Kasevich and Chu pioneered
the use of quantum physics for gravity gradient measurements. Since then
cold-atom gravity gradiometers, or matter-wave gravity gradiometers, had been
under development at almost every physics department of top-rated universities
around the globe. After another 30 years since the Kasevich and Chu publication
in 1992, which had led to the first ever quantum gravity gradiometer, the
corresponding research and development ceased from being profoundly active a
few years back. This article is an attempt to understand and explain what may
have happened to the Quantum Invasion into the area of applied physics and
precision engineering that traditionally has been occupied by non-quantum
technologies developed for about a 130 years of the history of gravity
gradiometry.
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quant-ph
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On some one-dimensional quantum-mechanical models with a delta-potential
interaction: We discuss a systematic construction of dimensionless quantum-mechanical
equations. The process reduces the number of independent model parameters to a
minimum and, at the same time, provides the natural units of length, energy,
etc. in a clear, straightforward way. We compare this systematic procedure with
the widely adopted one that consists of setting $\hbar=1$. As illustrative
examples, we choose some simple one-dimensional models proposed recently for
the study of localized states in inhomogeneous media.
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quant-ph
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Modally Resolved Fabry-Perot Experiment with Semiconductor Waveguides: Based on the interaction between different spatial modes, semiconductor
Bragg-reflection waveguides provide a highly functional platform for non-linear
optics. Therefore, the control and engineering of the properties of each
spatial mode is essential. Despite the multimodeness of our waveguide, the
well-established Fabry-Perot technique for recording fringes in the optical
transmission spectrum can successfully be employed for a detailed linear
optical characterization when combined with Fourier analysis. A prerequisite
for the modal sensitivity is a finely resolved transmission spectrum that is
recorded over a broad frequency band. Our results highlight how the features of
different spatial modes, such as their loss characteristics and dispersion
properties, can be separated from each other allowing their comparison. The
mode-resolved measurements are important for optimizing the performance of such
multimode waveguides by tailoring the properties of their spatial modes.
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quant-ph
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An approximation scheme and non-Hermitian re-normalization for
description of atom-field system evolution: Interactions between a source of light and atoms are ubiquitous in nature.
The study of them is interesting on the fundamental level as well as for
applications. They are in the core of Quantum Information Processing tasks and
in Quantum Thermodynamics protocols. However, even for two-level atom
interacting with field in rotating wave approximation there exists no exact
solution. This touches as basic problem in quantum field theory, where we can
only calculate the transitions in the time asymptotic limits (i.e. minus and
plus infinity), while we are not able to trace the evolution. In this paper we
want to get more insight into the time evolution of a total system of a
two-level atom and a continuous-mode quantum field. We propose an
approximation, which we are able to apply systematically to each order of Dyson
expansion, resulting in greatly simplified formula for the evolution of the
combined system at any time. Our tools include a proposed novel, {\it
non-Hermitian} re-normalization method. As a sanity check, by applying our
framework, we derive the known optical Bloch equations.
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quant-ph
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Exceptional and Non-crystallographic Root Systems and the Kochen-Specker
Theorem: The Kochen-Specker theorem states that a 3-dimensional complex Euclidean
space admits a finite configuration of projective lines such that the
corresponding quantum observables (the orthogonal projectors) cannot be
assigned with 0 and 1 values in a classically consistent way. This paper shows
that the irreducible root systems of exceptional and of non-crystallographic
types are useful in constructing such configurations in other dimensions. The
cases $E_6$ and $E_7$ lead to new examples, while $F_4$, $E_8$, and $H_4$,
yield a new interpretation of the known ones. The described configurations have
an additional property: they are saturated, i.e. the tuples of mutually
orthogonal lines, being partially ordered by inclusion, yield a poset with all
maximal elements having the same cardinality (the dimension of space).
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quant-ph
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Exciton Interferometry: An exciton beam splitter is designed and computationally implemented,
offering the prospect of excitonic interferometry. Exciton interaction between
propagation conduits is modeled using a coupling parameter that varies with
position. In practice, this variation can be realized by a change in the
distance separating conduits as would occur if they crossed at oblique angles.
Two such excitonic beam splitters can be combined to comprise an excitonic
analog to a Mach-Zehnder interferometer, allowing the relative phase shift
between two signals to be used to tailor the output populations on each
channel. In contrast to optical splitters, an excitonic signal can be
coherently split among more than two channels. These ideas are computationally
demonstrated within an idealized setting in which each site is idealized as a
two-level system. Physical implementations include molecular and coupled cavity
settings as well as combinations of these. This adds to the developing
inventory of excitonic analogs to optical elements.
|
quant-ph
|
Spatial distribution of electric field of equal probability quantum
walks based on three-level quantum system: Based on the three-level quantum system, when it is in resonance, according
to any two lattice points closest to Hamiltonian coupling, electrons transition
from high energy level to low energy level and release photons; Or absorb
photons and transition from low energy level to high energy level, thus
obtaining the physical process of quantum walking along a straight line under
the condition of equal probability. Then, the optical radiation in the quantum
walk is mapped into a Gaussian pulse of the electric field, and the Maxwell's
equation is solved by the three dimensional finite-difference time-domain
method to obtain the spatial electric distributio. Finally, the physical
process ofquantum walking on two parallel lines is further discussed, involving
some physical properties such as electromagnetic coupling or coherence, quantum
state exchange and so on. The electric field coupling between two lines can be
calculated by FDTD, which provides a useful tool for the design and analysis of
quantum devices.
|
quant-ph
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Memory Effects in Quantum Processes: Understanding temporal processes and their correlations in time is of
paramount importance for the development of near-term technologies that operate
under realistic conditions. Capturing the complete multi-time statistics
defining a stochastic process lies at the heart of any proper treatment of
memory effects. In this thesis, using a novel framework for the
characterisation of quantum stochastic processes, we first solve the long
standing question of unambiguously describing the memory length of a quantum
processes. This is achieved by constructing a quantum Markov order condition
that naturally generalises its classical counterpart for the quantification of
finite-length memory effects. As measurements are inherently invasive in
quantum mechanics, one has no choice but to define Markov order with respect to
the interrogating instruments that are used to probe the process at hand:
different memory effects are exhibited depending on how one addresses the
system, in contrast to the standard classical setting. We then fully
characterise the structural constraints imposed on quantum processes with
finite Markov order, shedding light on a variety of memory effects that can
arise through various examples. Lastly, we introduce an instrument-specific
notion of memory strength that allows for a meaningful quantification of the
temporal correlations between the history and the future of a process for a
given choice of experimental intervention. These findings are directly relevant
to both characterising and exploiting memory effects that persist for a finite
duration. In particular, immediate applications range from developing efficient
compression and recovery schemes for the description of quantum processes with
memory to designing coherent control protocols that efficiently perform
information-theoretic tasks, amongst a plethora of others.
|
quant-ph
|
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