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The Dynamical Mechanism of the Aharonov-Bohm Effect: In this paper, it is emphasized that the dynamical cause for the A-B effect
is the superimposed energy between the magnetic field produced by the moving
charges and that in the solenoid, instead of the existence of the vector
potential. If such a superposition between the magnetic fields can be
eliminated, the A-B effect should not be observed any more. To verify this
viewpoint, a new experimental method using a SQUID is suggested in this paper.
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quant-ph
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Quantum confinement in 1D systems through an imaginary-time evolution
method: Quantum confinement is studied by numerically solving time-dependent
Schr\"odinger equation. An imaginary-time evolution technique is employed in
conjunction with the minimization of an expectation value, to reach the global
minimum. Excited states are obtained by imposing the orthogonality constraint
with all lower states. Applications are made on three important model quantum
systems, namely, harmonic, repulsive and quartic oscillators; enclosed inside
an impenetrable box. The resulting diffusion equation is solved using
finite-difference method. Both symmetric and asymmetric confinement are
considered for attractive potential; for others only symmetrical confinement.
Accurate eigenvalue, eigenfunction and position expectation values are
obtained, which show excellent agreement with existing literature results.
Variation of energies with respect to box length is followed for small,
intermediate and large sizes. In essence a simple accurate and reliable method
is proposed for confinement in quantum systems.
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quant-ph
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Bounds for the adiabatic approximation with applications to quantum
computation: We present straightforward proofs of estimates used in the adiabatic
approximation. The gap dependence is analyzed explicitly. We apply the result
to interpolating Hamiltonians of interest in quantum computing.
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quant-ph
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Spontaneous emission of a moving atom in the presence of
magnetodielectric material: A relativistic approach: In this paper, based on a canonical quantization scheme, we study the effect
of the relativistic motion of an excited atom on its decay rate in the presence
of absorbing and dispersive media. For this purpose, we introduce an
appropriate Lagrangian and describe the center-of-mass dynamical variables by
the Dirac field. We obtain the Hamiltonian of the system in a multipolar form
and calculate the motion equations of the system in the Schr\"odinger picture.
We find that the decay rate and the quantum electrodynamics level shift of the
moving atom can be expressed in terms of the imaginary part of the classical
Green tensor and the center-of-mass velocity of the atom.
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quant-ph
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Laplacian versus Adjacency Matrix in Quantum Walk Search: A quantum particle evolving by Schr\"odinger's equation contains, from the
kinetic energy of the particle, a term in its Hamiltonian proportional to
Laplace's operator. In discrete space, this is replaced by the discrete or
graph Laplacian, which gives rise to a continuous-time quantum walk. Besides
this natural definition, some quantum walk algorithms instead use the adjacency
matrix to effect the walk. While this is equivalent to the Laplacian for
regular graphs, it is different for non-regular graphs, and is thus an
inequivalent quantum walk. We algorithmically explore this distinction by
analyzing search on the complete bipartite graph with multiple marked vertices,
using both the Laplacian and adjacency matrix. The two walks differ
qualitatively and quantitatively in their required jumping rate, runtime,
sampling of marked vertices, and in what constitutes a natural initial state.
Thus the choice of the Laplacian or adjacency matrix to effect the walk has
important algorithmic consequences.
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quant-ph
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Quantum Federated Learning with Quantum Data: Quantum machine learning (QML) has emerged as a promising field that leans on
the developments in quantum computing to explore large complex machine learning
problems. Recently, some purely quantum machine learning models were proposed
such as the quantum convolutional neural networks (QCNN) to perform
classification on quantum data. However, all of the existing QML models rely on
centralized solutions that cannot scale well for large-scale and distributed
quantum networks. Hence, it is apropos to consider more practical quantum
federated learning (QFL) solutions tailored towards emerging quantum network
architectures. Indeed, developing QFL frameworks for quantum networks is
critical given the fragile nature of computing qubits and the difficulty of
transferring them. On top of its practical momentousness, QFL allows for
distributed quantum learning by leveraging existing wireless communication
infrastructure. This paper proposes the first fully quantum federated learning
framework that can operate over quantum data and, thus, share the learning of
quantum circuit parameters in a decentralized manner. First, given the lack of
existing quantum federated datasets in the literature, the proposed framework
begins by generating the first quantum federated dataset, with a hierarchical
data format, for distributed quantum networks. Then, clients sharing QCNN
models are fed with the quantum data to perform a classification task.
Subsequently, the server aggregates the learnable quantum circuit parameters
from clients and performs federated averaging. Extensive experiments are
conducted to evaluate and validate the effectiveness of the proposed QFL
solution. This work is the first to combine Google's TensorFlow Federated and
TensorFlow Quantum in a practical implementation.
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quant-ph
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Complete controllability of finite quantum systems with two-fold energy
level degeneracy: Complete controllability of finite dimensional quantum systems with energy
level degeneracy is investigated using two different approaches. One approach
is to apply a weak constant field to eliminate the degeneracy and then control
it using techniques developed for non-degenerate quantum systems. Conditions
for the elimination of degeneracy are found and the issue of influence of
relaxation time of constant external field to the target state are addressed
through the fidelity. Another approach is to control the degenerate system by a
single control field directly. It is found that the system with two-fold
degenerate excited states and non-degenerate ground state are completely
controllable except for the two-level system. Conditions of complete
controllability are found for both systems with different energy gaps and with
equal energy gaps.
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quant-ph
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Equivariant Variational Quantum Eigensolver to detect Phase Transitions
through Energy Level Crossings: Level spectroscopy stands as a powerful method for identifying the transition
point that delineates distinct quantum phases. Since each quantum phase
exhibits a characteristic sequence of excited states, the crossing of energy
levels between low-lying excited states offers a reliable mean to estimate the
phase transition point. While approaches like the Variational Quantum
Eigensolver are useful for approximating ground states of interacting systems
using quantum computing, capturing low-energy excitations remains challenging.
In our study, we introduce an equivariant quantum circuit that preserves the
total spin and the translational symmetry to accurately describe singlet and
triplet excited states in the $J_1$-$J_2$ Heisenberg model on a chain, which
are crucial for characterizing its transition point. Additionally, we assess
the impact of noise on the variational state, showing that conventional
mitigation techniques like Zero Noise Extrapolation reliably restore its
physical properties.
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quant-ph
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The GEO600 squeezed light source: The next upgrade of the GEO600 gravitational wave detector is scheduled for
2010 and will, in particular, involve the implementation of squeezed light. The
required non-classical light source is assembled on a 1.5m^2 breadboard and
includes a full coherent control system and a diagnostic balanced homodyne
detector. Here, we present the first experimental characterization of this
setup as well as a detailed description of its optical layout. A squeezed
quantum noise of up to 9dB below the shot-noise level was observed in the
detection band between 10Hz and 10kHz. We also present an analysis of the
optical loss in our experiment and provide an estimation of the possible
non-classical sensitivity improvement of the future squeezed light enhanced
GEO600 detector.
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quant-ph
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General Quantum Bernoulli Factory: Framework Analysis and Experiments: The unremitting pursuit for quantum advantages gives rise to the discovery of
a quantum-enhanced randomness processing named quantum Bernoulli factory (QBF).
This quantum enhanced process can show its priority over the corresponding
classical process through readily available experimental resources, thus in the
near term it may be capable of accelerating the applications of classical
Bernoulli factories, such as the widely used sampling algorithms. In this work,
we provide the framework analysis of the QBF. We thoroughly analyze the quantum
state evolution in this process, discovering the field structure of the
constructible quantum states. Our framework analysis shows that naturally, the
previous works can be described as specific instances of this framework. Then,
as a proof of principle, we experimentally demonstrate this framework via an
entangled two-photon source along with a reconfigurable photonic logic, and
show the advantages of the QBF over the classical model through a classically
infeasible instance. These results may stimulate the discovery of advantages of
the quantum randomness processing in a wider range of tasks, as well as its
potential applications.
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quant-ph
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The role of spin in entanglement generated by expanding spacetime: We investigate the effects of spin on entanglement arising in Dirac field in
an expanding spacetime characterized by the Robertson-Walker metric. We present
a general approach that allows us to treat the case where only charge
conservation is required, as well as the case where also angular momentum
conservation is required. We fiend that in both situations entanglement,
quantified by subsystem entropy, behaves the same and does not qualitatively
deviates from the spinless case. Differences only arise when particles and/or
antiparticles are present in the input state.
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quant-ph
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Wigner Functions with Boundaries: We consider the general Wigner function for a particle confined to a finite
interval and subject to Dirichlet boundary conditions. We derive the boundary
corrections to the "star-genvalue" equation and to the time evolution equation.
These corrections can be cast in the form of a boundary potential contributing
to the total Hamiltonian which together with a subsidiary boundary condition is
responsible for the discretization of the energy levels. We show that a
completely analogous formulation (in terms of boundary potentials) is also
possible in standard operator quantum mechanics and that the Wigner and the
operator formulations are also in one-to-one correspondence in the confined
case. In particular, we extend Baker's converse construction to bounded
systems. Finally, we elaborate on the applications of the formalism to the
subject of Wigner trajectories, namely in the context of collision processes
and quantum systems displaying chaotic behavior in the classical limit.
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quant-ph
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When to Reject a Ground State Preparation Algorithm: In recent years substantial research effort has been devoted to quantum
algorithms for ground state energy estimation (GSEE) in chemistry and
materials. Given the many heuristic and non-heuristic methods being developed,
it is challenging to assess what combination of these will ultimately be used
in practice. One important metric for assessing utility is runtime. For most
GSEE algorithms, the runtime depends on the ground state preparation (GSP)
method. Towards assessing the utility of various combinations of GSEE and GSP
methods, we asked under which conditions a GSP method should be accepted over a
reference method, such as the Hartree-Fock state. We introduce a criteria for
accepting or rejecting a GSP method for the purposes of GSEE. We consider
different GSP methods ranging from heuristics to algorithms with provable
performance guarantees and perform numerical simulations to benchmark their
performance on different chemical systems, starting from small molecules like
the hydrogen atom to larger systems like the jellium. In the future this
approach may be used to abandon certain VQE ansatzes and other heursitics. Yet
so far our findings do not provide evidence against the use of VQE and more
expensive heuristic methods, like the low-depth booster. This work sets a
foundation from which to further explore the requirements to achieve quantum
advantage in quantum chemistry.
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quant-ph
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Hierarchy of Steering Criteria Based on Moments for All Bipartite
Quantum Systems: Einstein-Podolsky-Rosen steering is a manifestation of quantum correlations
exhibited by quantum systems, that allows for entanglement certification when
one of the subsystems is not characterized. Detecting steerability of quantum
states is essential to assess their suitability for quantum information
protocols with partially trusted devices. We provide a hierarchy of sufficient
conditions for the steerability of bipartite quantum states of any dimension,
including continuous variable states. Previously known steering criteria are
recovered as special cases of our approach. The proposed method allows us to
derive optimal steering witnesses for arbitrary families of quantum states, and
provides a systematic framework to analytically derive non-linear steering
criteria. We discuss relevant examples and, in particular, provide an optimal
steering witness for a lossy single-photon Bell state; the witness can be
implemented just by linear optics and homodyne detection, and detects steering
with a higher loss tolerance than any other known method. Our approach is
readily applicable to multipartite steering detection and to the
characterization of joint measurability.
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quant-ph
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Entanglement Degree of Parasupersymmetric Coherent States of Harmonic
Oscillator: We study the boson-parafermion entanglement of the parasupersymmetric
coherent states of the harmonic oscillator and derive the degree of
entanglement in terms of the concurrence. The conditions for obtaining the
maximal entanglement is also examined, and it is shown that in the usual
supersymmetry situation we can obtain maximally entangled Bell states.
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quant-ph
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Multichromatic Floquet engineering of quantum dissipation: The monochromatic driving of a quantum system is a successful technique in
quantum simulations, well captured by an effective Hamiltonian approach, and
with applications in artificial gauge fields and topological engineering. In
this letter, we investigate the modeling of multichromatic Floquet driving for
the slow degrees of freedom. Within a well-defined range of parameters, we show
that the time coarse-grained dynamics of such a driven closed quantum system is
encapsulated in an effective Master equation for the time-averaged density
matrix, that evolves under the action of an effective Hamiltonian and tunable
Lindblad-type dissipation/quantum gain terms. As an application, we emulate the
dissipation induced by phase noise and incoherent emission/absorption processes
in the bichromatic driving of a two-level system.
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quant-ph
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Codekets: To every binary linear [n,k]-code C we associate a quantum state ("codeket")
belonging to the n-th tensor power of the 2-dimensional complex Hilbert space
associated to the spin 1/2 particle. We completely characterize the expectation
values of the products of x-, y- or z- spins measured in the state we define,
for each of the particles in a chosen subset. This establishes an interesting
relationship with the dual code. We also address the case of nonlinear codes,
and derive both a bound satisfied by the expectations of spin products, as well
as a nice algebraic identity.
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quant-ph
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Ghost Imaging with Blackbody Radiation: We present a theoretical study of ghost imaging by using blackbody radiation
source. A Gaussian thin lens equation for the ghost imaging, which depends on
both paths, is derived. The dependences of the visibility and quality of the
image on the transverse size and temperature of the blackbody are studied. The
main differences between the ghost imaging by using the blackbody radiation and
by using the entangled photon pairs are image-forming equation, and the
visibility and quality of the image
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quant-ph
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Multiple teleportation via the partially entangled states: We investigate the multiple teleportation with some nonmaximally entangled
channels. The efficiencies of two multiple teleportation protocols, the
separate multiple teleportation protocol (SMTP) and the global multiple
teleportation protocol (GMTP), are calculated. We show that GMTP is more
efficient than SMTP.
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quant-ph
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On the descriptive power of Neural-Networks as constrained Tensor
Networks with exponentially large bond dimension: In many cases, Neural networks can be mapped into tensor networks with an
exponentially large bond dimension. Here, we compare different sub-classes of
neural network states, with their mapped tensor network counterpart for
studying the ground state of short-range Hamiltonians. We show that when
mapping a neural network, the resulting tensor network is highly constrained
and thus the neural network states do in general not deliver the naive expected
drastic improvement against the state-of-the-art tensor network methods. We
explicitly show this result in two paradigmatic examples, the 1D ferromagnetic
Ising model and the 2D antiferromagnetic Heisenberg model, addressing the lack
of a detailed comparison of the expressiveness of these increasingly popular,
variational ans\"atze.
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quant-ph
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From communication complexity to an entanglement spread area law in the
ground state of gapped local Hamiltonians: In this work, we make a connection between two seemingly different problems.
The first problem involves characterizing the properties of entanglement in the
ground state of gapped local Hamiltonians, which is a central topic in quantum
many-body physics. The second problem is on the quantum communication
complexity of testing bipartite states with EPR assistance, a well-known
question in quantum information theory. We construct a communication protocol
for testing (or measuring) the ground state and use its communication
complexity to reveal a new structural property for the ground state
entanglement. This property, known as the entanglement spread, roughly measures
the ratio between the largest and the smallest Schmidt coefficients across a
cut in the ground state. Our main result shows that gapped ground states
possess limited entanglement spread across any cut, exhibiting an "area law"
behavior. Our result quite generally applies to any interaction graph with an
improved bound for the special case of lattices. This entanglement spread area
law includes interaction graphs constructed in [Aharonov et al., FOCS'14] that
violate a generalized area law for the entanglement entropy. Our construction
also provides evidence for a conjecture in physics by Li and Haldane on the
entanglement spectrum of lattice Hamiltonians [Li and Haldane, PRL'08]. On the
technical side, we use recent advances in Hamiltonian simulation algorithms
along with quantum phase estimation to give a new construction for an
approximate ground space projector (AGSP) over arbitrary interaction graphs.
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quant-ph
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Consistent theory for causal non-locality beyond Born's rule: According to the theory of relativity and causality, a special type of
correlation beyond quantum mechanics is possible in principle under the name of
{\it non-local box}. The concept has been introduced from the principle of
non-locality which satisfies relativistic causality. In this paper, we show
that a correlation leading to the non-local box is possible to be derived
consistently if we release the one of major axioms in quantum mechanics, {\it
Born's rule}. This allows us to obtain a theory which in one end of the
spectrum agrees with the classical probability and in the other end, agrees
with the theory of non-local causality. At the same time, we argue that the
correlation lies in a space with special mathematical constraints such that a
physical realization of the correlation through a probability measure is not
possible in one direction of its limit and is possible in the other limit.
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quant-ph
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Projective characterization of higher-order quantum transformations: Transformations of transformations, also called higher-order transformations,
is a natural concept in information processing, which has recently attracted
significant interest in the study of quantum causal relations. In this work, a
framework for characterizing higher-order quantum transformations which relies
on the use of superoperator projectors is presented. More precisely, working
with projectors in the Choi-Jamiolkowski picture is shown to provide a handy
way of defining the characterization constraints on any class of higher-order
transformations. The algebraic properties of these projectors are furthermore
identified as a model of multiplicative additive linear logic (MALL). The main
novelty of this work is the introduction in the algebra of the 'prec'
connector. It is used for the characterization of maps that are no signaling
from input to output or the other way around. This allows to assess the
possible signaling structure of any maps characterized within the projective
framework. The properties of the prec are moreover shown to yield a canonical
form for projective expressions. This provides an unambiguous way to compare
different higher-order theories.
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quant-ph
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Complexity Classification of Product State Problems for Local
Hamiltonians: Product states, unentangled tensor products of single qubits, are a
ubiquitous ansatz in quantum computation, including for state-of-the-art
Hamiltonian approximation algorithms. A natural question is whether we should
expect to efficiently solve product state problems on any interesting families
of Hamiltonians.
We completely classify the complexity of finding minimum-energy product
states for Hamiltonians defined by any fixed set of allowed 2-qubit
interactions. Our results follow a line of work classifying the complexity of
solving Hamiltonian problems and classical constraint satisfaction problems
based on the allowed constraints. We prove that estimating the minimum energy
of a product state is in P if and only if all allowed interactions are 1-local,
and NP-complete otherwise. Equivalently, any family of non-trivial two-body
interactions generates Hamiltonians with NP-complete product-state problems.
Our hardness constructions only require coupling strengths of constant
magnitude.
A crucial component of our proofs is a collection of hardness results for a
new variant of the Vector Max-Cut problem, which should be of independent
interest. Our definition involves sums of distances rather than squared
distances and allows linear stretches.
A corollary of our classification is a new proof that optimizing product
states in the Quantum Max-Cut model (the quantum Heisenberg model) is
NP-complete.
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quant-ph
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Optimization of Lattice Surgery is NP-Hard: The traditional method for computation in either the surface code or in the
Raussendorf model is the creation of holes or "defects" within the encoded
lattice of qubits that are manipulated via topological braiding to enact logic
gates. However, this is not the only way to achieve universal, fault-tolerant
computation. In this work, we focus on the Lattice Surgery representation,
which realizes transversal logic operations without destroying the intrinsic 2D
nearest-neighbor properties of the braid-based surface code and achieves
universality without defects and braid based logic. For both techniques there
are open questions regarding the compilation and resource optimization of
quantum circuits. Optimization in braid-based logic is proving to be difficult
and the classical complexity associated with this problem has yet to be
determined. In the context of lattice-surgery-based logic, we can introduce an
optimality condition, which corresponds to a circuit with the lowest resource
requirements in terms of physical qubits and computational time, and prove that
the complexity of optimizing a quantum circuit in the lattice surgery model is
NP-hard.
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quant-ph
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Experimental optimal cloning of four-dimensional quantum states of
photons: Optimal quantum cloning is the process of making one or more copies of an
arbitrary unknown input quantum state with the highest possible fidelity. All
reported demonstrations of quantum cloning have so far been limited to copying
two-dimensional quantum states, or qubits. We report the experimental
realization of the optimal quantum cloning of four-dimensional quantum states,
or ququarts, encoded in the polarization and orbital angular momentum degrees
of freedom of photons. Our procedure, based on the symmetrization method, is
also shown to be generally applicable to quantum states of arbitrarily high
dimension -- or qudits -- and to be scalable to an arbitrary number of copies,
in all cases remaining optimal. Furthermore, we report the bosonic coalescence
of two single-particle entangled states.
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quant-ph
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Efficient Learning of Quantum States Prepared With Few Non-Clifford
Gates II: Single-Copy Measurements: Recent work has shown that $n$-qubit quantum states output by circuits with
at most $t$ single-qubit non-Clifford gates can be learned to trace distance
$\epsilon$ using $\mathsf{poly}(n,2^t,1/\epsilon)$ time and samples. All prior
algorithms achieving this runtime use entangled measurements across two copies
of the input state. In this work, we give a similarly efficient algorithm that
learns the same class of states using only single-copy measurements.
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quant-ph
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Teleportation with Multiple Accelerated Partners: As the current revolution in communication is underway, quantum teleportation
can increase the level of security in quantum communication applications. In
this paper, we present a quantum teleportation procedure that capable to
teleport either accelerated or non-accelerated information through different
quantum channels. These quantum chan- nels are based on accelerated multi-qubit
states, where each qubit of each of these channels represent a partner. Namely,
these states are the the W state, Greenberger-Horne-Zeilinger (GHZ) state, and
the GHZ-like state. Here, we show that the fidelity of teleporting acceler-
ated information is higher than the fidelity of teleporting non-accelerated
information, both through a quantum channel that is based on accelerated state.
Also, the comparison among the performance of these three channels shows that
the degree of fidelity depends on type of the used channel, type of the
measurement, and value of the acceleration. The result of comparison concludes
that teleporting information through channel that is based on the GHZ state is
more robust than teleporting information through channels that are based on the
other two states. For future work, the proposed procedure can be generalized
later to achieve communication through a wider quantum network.
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quant-ph
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What is wrong with von Neumann's theorem on "no hidden variables": It is shown that, although correct mathematically, the celebrated 1932
theorem of von Neumann which is often interpreted as proving the impossibility
of the existence of "hidden variables" in Quantum Mechanics, is in fact based
on an assumption which is physically not reasonable. Apart from that, the
alleged conclusion of von Neumann proving the impossibility of the existence of
"hidden variables" was already set aside in 1952 by the counterexample of the
possibility of a physical theory, such as given by what is usually called the
"Bohmian Mechanics". Similar arguments apply to other two well known
mathematical theorems, namely, of Gleason, and of Kochen and Specker, which
have often been seen as equally proving the impossibility of the existence of
"hidden variables" in Quantum Mechanics.
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quant-ph
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The quantum brachistochrone problem for an arbitrary spin in a magnetic
field: We consider quantum brachistochrone evolution for a spin-$s$ system on
rotational manifolds. Such manifolds are determined by the rotation of the
eigenstates of the operator of projection of spin-$s$ on some direction. The
Fubini-Study metrics of these manifolds are those of spheres with radii
dependent on the value of the spin and on the value of the spin projection. The
conditions for optimal evolution of the spin-$s$ system on rotational manifolds
are obtained.
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quant-ph
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Wavelength-scale errors in optical localization due to spin-orbit
coupling of light: The precise determination of the position of point-like emitters and
scatterers using far-field optical imaging techniques is of utmost importance
for a wide range of applications in medicine, biology, astronomy, and physics.
Although the optical wavelength sets a fundamental limit to the image
resolution of unknown objects, the position of an individual emitter can in
principle be estimated from the image with arbitrary precision. This is used,
e.g., in stars' position determination and in optical super-resolution
microscopy. Furthermore, precise position determination is an experimental
prerequisite for the manipulation and measurement of individual quantum
systems, such as atoms, ions, and solid state-based quantum emitters. Here we
demonstrate that spin-orbit coupling of light in the emission of elliptically
polarized emitters can lead to systematic, wavelength-scale errors in the
estimate of the emitter's position. Imaging a single trapped atom as well as a
single sub-wavelength-diameter gold nanoparticle, we demonstrate a shift
between the emitters' measured and actual positions which is comparable to the
optical wavelength. Remarkably, for certain settings, the expected shift can
become arbitrarily large. Beyond their relevance for optical imaging
techniques, our findings apply to the localization of objects using any type of
wave that carries orbital angular momentum relative to the emitter's position
with a component orthogonal to the direction of observation.
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quant-ph
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Perfect signaling among three parties violating predefined causal order: The paradigmatic view where information is seen as a more fundamental concept
than the laws of physics leads to a different understanding of spacetime where
the causal order of events emerges from correlations between random variables
representing physical quantities. In particular, such an information-theoretic
approach does not enforce a global spacetime structure. By following this path,
we conclude that perfect signaling correlations among three parties are
possible which do not obey the restrictions imposed by global spacetime. We
show this using a recent framework based on the sole assumptions that locally,
quantum theory is valid and random variables can be described by probability
distributions. Our result is of zero-error type and is an analog to a
tripartite appearance of quantum non-locality which manifests itself by
satisfying a condition with certainty whereas the same is impossible for any
local theory.
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quant-ph
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Dealing with unknown quantum operations: In the context of quantum communications between two parties (here Alice and
Bob), Bob's lack of knowledge about the communications channel can affect the
purity of the states that he receives. The operation of applying an unknown
unitary transformation to a state, thus reducing its purity, is called
"twirling". As twirling affects the states that Bob receives, it also affects
his perception of the operations that Alice applies to her states. In this work
we find that not every operation is representable after a twirling, we show the
minimal requirement for this to be possible, and we identify the correct form
of the "twirled" operations.
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quant-ph
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Ultra-coherent nanomechanical resonators via soft clamping and
dissipation dilution: The small mass and high coherence of nanomechanical resonators render them
the ultimate force probe, with applications ranging from biosensing and
magnetic resonance force microscopy, to quantum optomechanics. A notorious
challenge in these experiments is thermomechanical noise related to dissipation
through internal or external loss channels. Here, we introduce a novel approach
to defining nanomechanical modes, which simultaneously provides strong spatial
confinement, full isolation from the substrate, and dilution of the resonator
material's intrinsic dissipation by five orders of magnitude. It is based on a
phononic bandgap structure that localises the mode, without imposing the
boundary conditions of a rigid clamp. The reduced curvature in the highly
tensioned silicon nitride resonator enables mechanical $Q>10^{8}$ at $ 1
\,\mathrm{MHz}$, yielding the highest mechanical $Qf$-products
($>10^{14}\,\mathrm{Hz}$) yet reported at room temperature. The corresponding
coherence times approach those of optically trapped dielectric particles.
Extrapolation to $4{.}2$ Kelvin predicts $\sim$quanta/ms heating rates, similar
to trapped ions.
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quant-ph
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Classical Optimizers for Noisy Intermediate-Scale Quantum Devices: We present a collection of optimizers tuned for usage on Noisy
Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of
applications in quantum computing, including the Variational Quantum
Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They
are also used for calibration tasks, hyperparameter tuning, in machine
learning, etc. We analyze the efficiency and effectiveness of different
optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical
minimizer step driving the next evaluation on the quantum processor. While most
results to date concentrated on tuning the quantum VQE circuit, we show that,
in the presence of quantum noise, the classical minimizer step needs to be
carefully chosen to obtain correct results. We explore state-of-the-art
gradient-free optimizers capable of handling noisy, black-box, cost functions
and stress-test them using a quantum circuit simulation environment with noise
injection capabilities on individual gates. Our results indicate that
specifically tuned optimizers are crucial to obtaining valid science results on
NISQ hardware, and will likely remain necessary even for future fault tolerant
circuits.
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quant-ph
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A localized quantum walk with a gap in distribution: Quantum walks behave differently from what we expect and their probability
distributions have unique structures. They have localization, singularities, a
gap, and so on. Those features have been discovered from the view point of
mathematics and reported as limit theorems. In this paper we focus on a
time-dependent three-state quantum walk on the line and demonstrate a limit
distribution. Three coin states at each position are iteratively updated by a
coin-flip operator and a position-shift operator. As the result of the
evolution, we end up to observe both localization and a gap in the limit
distribution.
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quant-ph
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Nonreciprocal photon blockade via quadratic optomechanical coupling: We propose to manipulate the statistic properties of the photons transport
nonreciprocally via quadratic optomechanical coupling. We present a scheme to
generate quadratic optomechanical interactions in the normal optical modes of a
whispering-gallery-mode (WGM) optomechanical system by eliminating the linear
optomechanical couplings via anticrossing of different modes. By optically
pumping the WGM optomechanical system in one direction, the effective quadratic
optomechanical coupling in that direction will be enhanced significantly, and
nonreciprocal photon blockade will be observed consequently. Our proposal has
potential applications for the on-chip nonreciprocal single-photon devices.
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quant-ph
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On the Nature of Quantum Phenomena: It is shown that a coherent understanding of all quantized phenomena,
including those governed by unitary evolution equations as well as those
related to irreversible quantum measurements, can be achieved in a scenario of
successive nonequilibrium phase transitions, with the lowest hierarchy of these
phase transitions occurring in a ``resonant cavity'' formed by the entire
matter and energy content of the universe. In this formalism, the physical laws
themselves are resonantly-selected and ordered in the universe cavity in a
hierarchical manner, and the values of fundamental constants are determined
through a Generalized Mach's Principle. The existence of a preferred reference
frame in this scenario is shown to be consistent with the relational nature of
the origin of physical laws. Covariant unitary evolution is shown to connect
smoothly with the reduction of wavefunction in the preferred frame during
quantum measurement. The superluminal nature of quantum processes in the lowest
hierarchy coexists with the universal speed limit obeyed by processes in higher
hierarchies. A natural quantum-to-classical transition is also obtained which
is stable against the diffusive tendency of the unitary quantum evolution
processes. In this formalism a realistic quasi-classical ontology is
established for the foundations of quantum mechanics.
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quant-ph
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Notes on distinguishability of postselected computations: The framework of postselection is becoming more and more important in various
recent directions in Quantum Computation research. Postselection renders simple
computational models able to perform general quantum computation. This was
first observed for the linear optics model [E. Knill, R. Laflamme, G. J.
Milburn, Nature 409, 46 (2001)], and has since provided us with many near-term
candidates for the quantum advantage, commuting computations [M. J. Bremner, R.
Jozsa, D. J. Shepherd, Proc. R. Soc. A 467, 459 (2011)] being the first. To
facilitate the discussion of errors in the presence of postselection, we define
and characterize trace-induced distance and diamond distance of postselected
computations. We show counterexamples to simple properties that one would
expect of any distance measure; the properties of convexity (when considering
only the pure-state inputs would suffice), contractivity, and subadditivity of
errors. On the positive side, we prove that certain weaker versions of
contractivity and subadditivity and a number of other properties are preserved
in the postselected setting. We achieve this via a "conversion lemma" that
translates any inequality from the standard to the postselected setting.
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quant-ph
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A new method for constructing squeezed states for the isotropic 2D
harmonic oscillator: We introduce a new method for constructing squeezed states for the 2D
isotropic harmonic oscillator. Based on the construction of coherent states in
[1], we define a new set of ladder operators for the 2D system as a linear
combination of the x and y ladder operators and construct the SU(2) coherent
states. The new ladder operators are used for generalizing the squeezing
operator to 2D and the SU(2) coherent states play the role of the Fock states
in the expansion of the 2D squeezed states. We discuss some properties of the
2D squeezed states.
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quant-ph
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A comparative study of estimation methods in quantum tomography: As quantum tomography is becoming a key component of the quantum engineering
toolbox, there is a need for a deeper understanding of the multitude of
estimation methods available. Here we investigate and compare several such
methods: maximum likelihood, least squares, generalised least squares, positive
least squares, thresholded least squares and projected least squares. The
common thread of the analysis is that each estimator projects the measurement
data onto a parameter space with respect to a specific metric, thus allowing us
to study the relationships between different estimators.
The asymptotic behaviour of the least squares and the projected least squares
estimators is studied in detail for the case of the covariant measurement and a
family of states of varying ranks. This gives insight into the rank-dependent
risk reduction for the projected estimator, and uncovers an interesting
non-monotonic behaviour of the Bures risk. These asymptotic results complement
recent non-asymptotic concentration bounds of \cite{GutaKahnKungTropp} which
point to strong optimality properties, and high computational efficiency of the
projected linear estimators.
To illustrate the theoretical methods we present results of an extensive
simulation study. An app running the different estimators has been made
available online.
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quant-ph
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Engineering Giant Nonlinearities in Quantum Nanosystems: We describe a method to engineer giant nonlinearities in, and probes to
measure nonlinear observables of, mesoscopic quantum resonators. This involves
tailoring the Hamiltonian of a simple auxiliary system perturbatively coupled
to the resonator, and has the potential to engineer a wide range of
nonlinearities to high accuracy. We give a number of explicit examples,
including a readily realizable two-qubit auxiliary system that creates an x^4
potential and a Chi^(3) (Kerr) nonlinearity, valid to fifth-order in the
perturbative coupling.
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Effects of Lorentz boosts on Dirac bispinor entanglement: In this paper we describe the transformation properties of quantum
entanglement encoded in a pair of spin 1/2 particles described via Dirac
bispinors. Due to the intrinsic parity-spin internal structure of the
bispinors, the joint state is a four-qubit state exhibiting multipartite
entanglement, and to compute global correlation properties we consider the
averaged negativities over each possible bi-partition. We also consider
specific bipartitions, such as the spin-spin and the particle-particle
bipartitions. The particle-particle entanglement, between all degrees of
freedom of one particle and all degrees of freedom of the other particle, is
invariant under boosts if each particle has a definite momentum, although the
spin-spin entanglement is degraded for high speed boosts. Correspondingly, the
mean negativities are not invariant since the boost drives changes into
correlations encoded in specific bipartitions. Finally, the results presented
in the literature about spin-momentum entanglement are recovered by considering
the projection of bispinorial states into positive intrinsic parity, and some
striking differences between the appropriate approach for this case and the one
usually treated in the literature are discussed.
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quant-ph
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Continuous-time open quantum walks in one dimension: matrix-valued
orthogonal polynomials and Lindblad generators: We study continuous-time open quantum walks in one dimension through a matrix
representation, focusing on nearest-neighbor transitions for which an
associated weight matrix exists. Statistics such as site recurrence are studied
in terms of matrix-valued orthogonal polynomials and explicit calculations are
obtained for classes of Lindblad generators that model quantum versions of
birth-death processes. Emphasis is given to the technical distinction between
the cases of a finite or infinite number of vertices. Recent results for open
quantum walks are adapted in order to apply the folding trick to
continuous-time birth-death chains on the integers. Finally, we investigate the
matrix-valued Stieltjes transform associated to the weights.
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quant-ph
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Correlation functions in resonance fluorescence with spectral
resolution: Signal-processing approach: In the framework of the signal processing approach to single-atom resonance
fluorescence with spectral resolution, we diagrammatically derive an analytical
formula for arbitrary-order spectral correlation functions of the scattered
fields that pass through Fabry-Perot interferometers. Our general expression is
then applied to study correlation signals in the limit of well separated
spectral lines of the resonance fluorescence spectrum. In particular, we study
the normalized second-order temporal intensity correlation functions in the
case of the interferometers tuned to the components of the spectrum and obtain
interferential corrections to the approximate results derived in the secular
limit. In addition, we explore purely spectral correlations and show that they
can fully be understood in terms of the two-photon cascades down the dressed
state ladder.
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quant-ph
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Extending Noether's theorem by quantifying the asymmetry of quantum
states: Noether's theorem is a fundamental result in physics stating that every
symmetry of the dynamics implies a conservation law. It is, however, deficient
in several respects: (i) it is not applicable to dynamics wherein the system
interacts with an environment, and (ii) even in the case where the system is
isolated, if the quantum state is mixed then the Noether conservation laws do
not capture all of the consequences of the symmetries. To address these
deficiencies, we introduce measures of the extent to which a quantum state
breaks a symmetry. Such measures yield novel constraints on state transitions:
for nonisolated systems, they cannot increase, while for isolated systems they
are conserved. We demonstrate that the problem of finding nontrivial asymmetry
measures can be solved using the tools of quantum information theory.
Applications include deriving model-independent bounds on the quantum noise in
amplifiers and assessing quantum schemes for achieving high-precision
metrology.
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The separability versus entanglement problem: We present a review of the problem of finding out whether a quantum state of
two or more parties is entangled or separable. After a formal definition of
entangled states, we present a few criteria for identifying entangled states
and introduce some entanglement measures. We also provide a classification of
entangled states with respect to their usefulness in quantum dense coding, and
present some aspects of multipartite entanglement.
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quant-ph
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Asymmetric wave functions from tiny perturbations: The quantum mechanical behavior of a particle in a double well defies our
intuition based on classical reasoning. Not surprisingly, an asymmetry in the
double well will restore results more consistent with the classical picture.
What is surprising, however, is how a very small asymmetry can lead to
essentially classical behavior. In this paper we use the simplest version of a
double well potential to demonstrate these statements. We also show how this
system accurately maps onto a two-state system, which we refer to as a `toy
model'.
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quant-ph
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Integrating cavity quantum electrodynamics and ultracold-atom chips with
on-chip dielectric mirrors and temperature stabilization: We have fabricated an atom chip device which combines the circuitry for
magnetic trapping of cold atoms with high-finesse optical resonators suitable
for cavity QED in the single-atom strong coupling regime. Fabry-Perot optical
resonators with finesse F > 2 X 10^5 were formed between a micropatterned
on-chip planar mirror with lateral dimension of < 100 um and a curved mirror
suspended above the chip. The strong and rapid thermal coupling between on-chip
electrical and optical elements was utilized to stabilize the cavity mirror
separation with servo bandwidth exceeding 100 kHz during simulated operation of
the atom chip.
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quant-ph
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Quantum probe hyperpolarisation of molecular nuclear spins: The hyperpolarisation of nuclear spins within target molecules is a critical
and complex challenge in magnetic resonance imaging (MRI) and nuclear magnetic
resonance (NMR) spectroscopy. Hyperpolarisation offers enormous gains in signal
and spatial resolution which may ultimately lead to the development of
molecular MRI and NMR. At present, techniques used to polarise nuclear spins
generally require low temperatures and/or high magnetic fields, radio-frequency
control fields, or the introduction of catalysts or free-radical mediators. The
emergence of room temperature solid-state spin qubits has opened exciting new
pathways to circumvent these requirements to achieve direct nuclear spin
hyperpolarisation using quantum control. Employing a novel cross-relaxation
induced polarisation (CRIP) protocol using a single nitrogen-vacancy (NV)
centre in diamond, we demonstrate the first external nuclear spin
hyperpolarisation achieved by a quantum probe, in this case of $^1$H molecular
spins in poly(methyl methacrylate). In doing so, we show that a single qubit is
capable of increasing the thermal polarisation of $\sim 10^6$ nuclear spins by
six orders of magnitude, equivalent to an applied magnetic field of $10^5$\,T.
The technique can also be tuned to multiple spin species, which we demonstrate
using both \C{13} and $^1$H nuclear spin ensembles. Our results are analysed
and interpreted via a detailed theoretical treatment, which is also used to
describe how the system can be scaled up to a universal quantum
hyperpolarisation platform for the production of macroscopic quantities of
contrast agents at high polarisation levels for clinical applications. These
results represent a new paradigm for nuclear spin hyperpolarisation for
molecular imaging and spectroscopy, and beyond into areas such as materials
science and quantum information processing.
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quant-ph
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Cavity-induced anti-correlated photon emission rates of a single ion: We report on the alteration of photon emission properties of a single trapped
ion coupled to a high finesse optical fiber cavity. We show that the vacuum
field of the cavity can simultaneously affect the emissions in both the
infrared (IR) and ultraviolet (UV) branches of the $\Lambda-$type level system
of $^{40}\mathrm{Ca}^+$ despite the cavity coupling only to the IR transition.
The cavity induces strong emission in the IR transition through the Purcell
effect resulting in a simultaneous suppression of the UV fluorescence. The
measured suppression of this fluorescence is as large as 66% compared with the
case without the cavity. Through analysis of the measurement results, we have
obtained an ion-cavity coupling of $\bar{g}_0 = 2\pi\cdot (5.3 \pm 0.1)$ MHz,
the largest ever reported so far for a single ion in the IR domain.
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quant-ph
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Informationally complete measures of quantum entanglement: Although quantum entanglement has already been verified experimentally and
applied in quantum computing, quantum sensing and quantum networks, most of the
existing measures cannot characterize the entanglement faithfully. In this
work, by exploiting the Schmidt decomposition of a bipartite state
$|\psi\rangle_{AB}$, we first establish a one-to-one correspondence relation
between the characteristic polynomial of the reduced state $\rho_A$ and the
polynomials its trace. Then we introduce a family of entanglement measures
which are given by the complete eigenvalues of the reduced density matrices of
the system. Specific measures called informationally complete entanglement
measures (ICEMs) are presented to illustrate the advantages. It is demonstrated
that such ICEMs can characterize finer and distinguish better the entanglement
than existing well-known entanglement measures. They also give rise to criteria
of state transformations under local operation and classical communication.
Moreover, we show that the ICEMs can be efficiently estimated on a quantum
computer. The fully separability, entanglement and genuine multipartite
entanglement can detected faithfully on quantum devices.
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quant-ph
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Retrodiction with two-level atoms: atomic previvals: In the Jaynes-Cummings model a two-level atom interacts with a single-mode
electromagnetic field. Quantum mechanics predicts collapses and revivals in the
probability that a measurement will show the atom to be excited at various
times after the initial preparation of the atom and field. In retrodictive
quantum mechanics we seek the probability that the atom was prepared in a
particular state given the initial state of the field and the outcome of a
later measurement on the atom. Although this is not simply the time reverse of
the usual predictive problem, we demonstrate in this paper that retrodictive
collapses and revivals also exist. We highlight the differences between
predictive and retrodictive evolutions and describe an interesting situation
where the prepared state is essentially unretrodictable.
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quant-ph
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A quantum solution to the arrow-of-time dilemma: reply: I acknowledge a flaw in the paper "A quantum solution to the arrow of time
dilemma": as pointed out by Jennings and Rudolph, (classical) mutual
information is not an appropriate measure of information. This can be traced
back to the quantum description underlying my analysis, where quantum mutual
information is the appropriate measure of information. The core argument of my
paper (summarized in its abstract) is not affected by this flaw. Nonetheless, I
point out that such argument may not be adequate to account for all phenomena:
it seems necessary to separately postulate a low entropy initial state.
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quant-ph
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Shortcut to adiabaticity in a Stern-Gerlach apparatus: We show that the performances of a Stern-Gerlach apparatus can be improved by
using a magnetic field profile for the atomic spin evolution designed through
shortcut to adiabaticity technique. Interestingly, it can be made more compact
- for atomic beams propagating at a given velocity - and more resilient to a
dispersion in velocity, in comparison with the results obtained with a standard
uniform rotation of the magnetic field. Our results are obtained using a
reverse engineering approach based on Lewis-Riesenfeld invariants. We discuss
quantitatively the advantages offered by our configuration in terms of the
resources involved and show that it drastically enhances the fidelity of the
quantum state transfer achieved by the Stern-Gerlach device.
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quant-ph
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Spin-orbit-coupled quantum memory of a double quantum dot: The concept of quantum memory plays an incisive role in the quantum
information theory. As confirmed by several recent rigorous mathematical
studies, the quantum memory inmate in the bipartite system $\rho_{AB}$ can
reduce uncertainty about the part $B$, after measurements done on the part $A$.
In the present work, we extend this concept to the systems with a spin-orbit
coupling and introduce a notion of spin-orbit quantum memory. We
self-consistently explore Uhlmann fidelity, pre and post measurement
entanglement entropy and post measurement conditional quantum entropy of the
system with spin-orbit coupling and show that measurement performed on the spin
subsystem decreases the uncertainty of the orbital part. The uncovered effect
enhances with the strength of the spin-orbit coupling. We explored the concept
of macroscopic realism introduced by Leggett and Garg and observed that POVM
measurements done on the system under the particular protocol are
non-noninvasive. For the extended system, we performed the quantum Monte Carlo
calculations and explored reshuffling of the electron densities due to the
external electric field.
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quant-ph
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Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar
Many-Body System: A discrete time crystal (DTC) is a robust phase of driven systems that breaks
the discrete time translation symmetry of the driving Hamiltonian. Recent
experiments have observed DTC signatures in two distinct systems. Here we show
nuclear magnetic resonance (NMR) observations of DTC signatures in a third,
strikingly different system: an ordered spatial crystal. We use a novel DTC
echo experiment to probe the coherence of the driven system. Finally, we show
that interactions during the pulse of the DTC sequence contribute to the decay
of the signal, complicating attempts to measure the intrinsic lifetime of the
DTC.
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quant-ph
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Imaging of high-frequency electromagnetic field by multipulse sensing
using nitrogen vacancy centers in diamond: Near-field enhancement of the microwave field is applied for imaging high
frequency radio field using a diamond chip with an $n$-doped isotopically
purified diamond layer grown by microwave plasma assisted chemical vapor
deposition. A short $\pi$ pulse length enables us to utilize a multipulse
dynamic decoupling method for detection of radio frequency field at 19.23 MHz.
An extraordinary frequency resolution of the external magnetic field detection
is achieved by using amplitude-shaped control pulses. Our method opens up the
possibility for high-frequency-resolution RF imaging at $\mu$m spatial
resolution using nitrogen vacancy centers in diamond.
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quant-ph
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Entanglement and nonlocality of a single relativistic particle: Recent work has argued that the concepts of entanglement and nonlocality must
be taken seriously even in systems consisting of only a single particle. These
treatments, however, are nonrelativistic and, if single particle entanglement
is fundamental, it should also persist in a relativistic description. Here we
consider a spin-1/2 particle in a superposition of two different velocities as
viewed by an observer in a different relativistically-boosted inertial frame.
We show that the entanglement survives right up to the speed of light and that
the boosted observer would see single-particle violations of Bell's inequality.
We also discuss how quantum gates could be implemented in this way and the
possible implications for quantum information processing.
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quant-ph
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The power of random measurements: measuring Tr(ρ^n) on single copies
of ρ: While it is known that Tr(\rho^n) can be measured directly (i.e., without
first reconstructing the density matrix) by performing joint measurements on n
copies of the same state rho, it is shown here that random measurements on
single copies suffice, too. Averaging over the random measurements directly
yields estimates of Tr(\rho^n), even when it is not known what measurements
were actually performed (so that one cannot reconstruct \rho).
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quant-ph
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Unconventional geometric quantum phase gates with a cavity QED system: We propose a scheme for realizing two-qubit quantum phase gates via an
unconventional geometric phase shift with atoms in a cavity. In the scheme the
atoms interact simultaneously with a highly detuned cavity mode and a classical
field. The atoms undergo no transitions during the gate operation, while the
cavity mode is displaced along a circle in the phase space, aquiring a
geometric phase conditional upon the atomic state. Under certain conditions,
the atoms are disentangled with the cavity mode and thus the gate is
insensitive to both the atomic spontaneous emission and the cavity decay.
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quant-ph
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Quantum error mitigation as a universal error-minimization technique:
applications from NISQ to FTQC eras: In the early years of fault-tolerant quantum computing (FTQC), it is expected
that the available code distance and the number of magic states will be
restricted due to the limited scalability of quantum devices and the
insufficient computational power of classical decoding units. Here, we
integrate quantum error correction and quantum error mitigation into an
efficient FTQC architecture that effectively increases the code distance and
$T$-gate count at the cost of constant sampling overheads in a wide range of
quantum computing regimes. For example, while we need $10^4$ to $10^{10}$
logical operations for demonstrating quantum advantages from optimistic and
pessimistic points of view, we show that we can reduce the required number of
physical qubits by $80\%$ and $45\%$ in each regime. From another perspective,
when the achievable code distance is up to about 11, our scheme allows
executing $10^3$ times more logical operations. This scheme will dramatically
alleviate the required computational overheads and hasten the arrival of the
FTQC era.
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quant-ph
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Discerning Elementary Particles: We extend the quantum-mechanical results of Muller & Saunders (2008)
establishing the weak discernibility of an arbitrary number of similar fermions
in finite-dimensional Hilbert-spaces in two ways: (a) from fermions to bosons
for all finite-dimensional Hilbert-spaces; and (b) from finite-dimensional to
infinite-dimensional Hilbert-spaces for all elementary particles. In both cases
this is performed using operators whose physical significance is beyond
doubt.This confutes the currently dominant view that (A) the quantum-mechanical
description of similar particles conflicts with Leibniz's Principle of the
Identity of Indiscernibles (PII); and that (B) the only way to save PII is by
adopting some pre-Kantian metaphysical notion such as Scotusian haecceittas or
Adamsian primitive thisness. We take sides with Muller & Saunders (2008)
against this currently dominant view, which has been expounded and defended by,
among others, Schr\"odinger, Margenau, Cortes, Dalla Chiara, Di Francia,
Redhead, French, Teller, Butterfield, Mittelstaedt, Giuntini, Castellani,
Krause and Huggett.
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quant-ph
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Gaussian ensembles distributions from mixing quantum systems: In the context of the mixing dynamical systems we present a derivation of the
Gaussian ensembles distributions from mixing quantum systems having a classical
analog that is mixing. We find that mixing factorization property is satisfied
for the mixing quantum systems expressed as a factorization of quantum mean
values. For the case of the kicked rotator and in its fully chaotic regime, the
factorization property links decoherence by dephasing with Gaussian ensembles
in terms of the weak limit, interpreted as a decohered state. Moreover, a
discussion about the connection between random matrix theory and quantum
chaotic systems, based on some attempts made in previous works and from the
viewpoint of the mixing quantum systems, is presented.
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quant-ph
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Accelerated quantum adiabatic transfer in superconducting qubits: Quantum adiabatic transfer is widely used in quantum computation and quantum
simulation. However, the transfer speed is limited by the quantum adiabatic
approximation condition, which hinders its application in quantum systems with
a short decoherence time. Here we demonstrate quantum adiabatic state transfers
that jump along geodesics in one-qubit and two-qubit superconducting transmons.
This approach possesses the advantages of speed, robustness, and high fidelity
compared with the usual adiabatic process. Our protocol provides feasible
strategies for improving state manipulation and gate operation in
superconducting quantum circuits.
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quant-ph
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Quantum walk coherences on a dynamical percolation graph: Coherent evolution governs the behaviour of all quantum systems, but in
nature it is often subjected to influence of a classical environment. For
analysing quantum transport phenomena quantum walks emerge as suitable model
systems. In particular, quantum walks on percolation structures constitute an
attractive platform for studying open system dynamics of random media. Here, we
present an implementation of quantum walks differing from the previous
experiments by achieving dynamical control of the underlying graph structure.
We demonstrate the evolution of an optical time-multiplexed quantum walk over
six double steps, revealing the intricate interplay between the internal and
external degrees of freedom. The observation of clear non-Markovian signatures
in the coin space testifies the high coherence of the implementation and the
extraordinary degree of control of all system parameters. Our work is the
proof-of-principle experiment of a quantum walk on a dynamical percolation
graph, paving the way towards complex simulation of quantum transport in random
media.
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quant-ph
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Anomalous Quantum Information Scrambling for $\mathbb{Z}_3$ Parafermion
Chains: Parafermions are exotic quasiparticles with non-Abelian fractional statistics
that could be exploited to realize universal topological quantum computing.
Here, we study the scrambling of quantum information in one-dimensional
parafermionic chains, with a focus on $\mathbb{Z}_3$ parafermions in
particular. We use the generalized out-of-time-ordered correlators (OTOCs) as a
measure of the information scrambling and introduce an efficient method based
on matrix product operators to compute them. With this method, we compute the
OTOCs for $\mathbb{Z}_3$ parafermions chains up to $200$ sites for the entire
early growth region. We find that, in stark contrast to the dynamics of
conventional fermions or bosons, the information scrambling light cones for
parafermions can be both symmetric and asymmetric, even for inversion-invariant
Hamiltonians involving only hopping terms. In addition, we find a deformed
light cone structure with a sharp peak at the boundary of the parafermion
chains in the topological regime, which gives a unambiguous evidence of the
strong zero modes at infinite temperature.
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quant-ph
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Superconducting quantum node for entanglement and storage of microwave
radiation: Superconducting circuits and microwave signals are good candidates to realize
quantum networks, which are the backbone of quantum computers. We have realized
a quantum node based on a 3D microwave superconducting cavity parametrically
coupled to a transmission line by a Josephson ring modulator. We first
demonstrate the time-controlled capture, storage and retrieval of an optimally
shaped propagating microwave field, with an efficiency as high as 80%. We then
demonstrate a second essential ability, which is the timed-controlled
generation of an entangled state distributed between the node and a microwave
channel.
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quant-ph
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Experimental Realization of a Quantum Autoencoder: The Compression of
Qutrits via Machine Learning: With quantum resources a precious commodity, their efficient use is highly
desirable. Quantum autoencoders have been proposed as a way to reduce quantum
memory requirements. Generally, an autoencoder is a device that uses machine
learning to compress inputs, that is, to represent the input data in a
lower-dimensional space. Here, we experimentally realize a quantum autoencoder,
which learns how to compress quantum data using a classical optimization
routine. We demonstrate that when the inherent structure of the data set allows
lossless compression, our autoencoder reduces qutrits to qubits with low error
levels. We also show that the device is able to perform with minimal prior
information about the quantum data or physical system and is robust to
perturbations during its optimization routine.
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quant-ph
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Entanglement from tensor networks on a trapped-ion QCCD quantum computer: The ability to selectively measure, initialize, and reuse qubits during a
quantum circuit enables a mapping of the spatial structure of certain
tensor-network states onto the dynamics of quantum circuits, thereby achieving
dramatic resource savings when using a quantum computer to simulate many-body
systems with limited entanglement. We experimentally demonstrate a significant
benefit of this approach to quantum simulation: In addition to all correlation
functions, the entanglement structure of an infinite system -- specifically the
half-chain entanglement spectrum -- is conveniently encoded within a small
register of "bond qubits" and can be extracted with relative ease. Using a
trapped-ion QCCD quantum computer equipped with selective mid-circuit
measurement and reset, we quantitatively determine the near-critical
entanglement entropy of a correlated spin chain directly in the thermodynamic
limit and show that its phase transition becomes quickly resolved upon
expanding the bond-qubit register.
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quant-ph
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A unitary quantum lattice gas algorithm for two dimensional quantum
turbulence: Quantum vortex structures and energy cascades are examined for two
dimensional quantum turbulence (2D QT) at zero temperature. A special unitary
evolution algorithm, the quantum lattice gas (QLG) algorithm, is employed to
simulate the Bose-Einstein condensate (BEC) governed by the Gross-Pitaevskii
(GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is
a short Poincar\'e recurrence time. It is demonstrated that such short
recurrence times are destroyed as the nonlinear interaction is strengthened.
The similar loss of Poincar\'e recurrence is also reported in 3D QT [1] Energy
cascades for 2D QT are considered to examine whether 2D QT exhibits inverse
cascades as in 2D classical turbulence. In the parameter regime considered, the
spectra analysis reveals no such dual cascades-dual cascades being a hallmark
of 2D classical turbulence.
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quant-ph
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Investigating Quantum Many-Body Systems with Tensor Networks, Machine
Learning and Quantum Computers: We perform quantum simulation on classical and quantum computers and set up a
machine learning framework in which we can map out phase diagrams of known and
unknown quantum many-body systems in an unsupervised fashion. The classical
simulations are done with state-of-the-art tensor network methods in one and
two spatial dimensions. For one dimensional systems, we utilize matrix product
states (MPS) that have many practical advantages and can be optimized using the
efficient density matrix renormalization group (DMRG) algorithm. The data for
two dimensional systems is obtained from entangled projected pair states (PEPS)
optimized via imaginary time evolution. Data in form of observables,
entanglement spectra, or parts of the state vectors from these simulations, is
then fed into a deep learning (DL) pipeline where we perform anomaly detection
to map out the phase diagram. We extend this notion to quantum computers and
introduce quantum variational anomaly detection. Here, we first simulate the
ground state and then process it in a quantum machine learning (QML) manner.
Both simulation and QML routines are performed on the same device, which we
demonstrate both in classical simulation and on a physical quantum computer
hosted by IBM.
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quant-ph
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Stronger Quantum Correlations with Loophole-free Post-selection: One of the most striking non-classical features of quantum mechanics is in
the correlations it predicts between spatially separated measurements. In local
hidden variable theories, correlations are constrained by Bell inequalities,
but quantum correlations violate these. However, experimental imperfections
lead to "loopholes" whereby LHV correlations are no longer constrained by Bell
inequalities, and violations can be described by LHV theories. For example,
loopholes can emerge through selective detection of events. In this letter, we
introduce a clean, operational picture of multi-party Bell tests, and show that
there exists a non-trivial form of loophole-free post-selection. Surprisingly,
the same post-selection can enhance quantum correlations, and unlock a
connection between non-classical correlations and non-classical computation.
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quant-ph
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q-Deformed Boson Oscillators and Zero Point Energy: Just as for the ordinary quantum harmonic oscillators, we expect the
zero-point energy to play a crucial role in the correct high temperature
behavior. We accordingly reformulate the theory of the statistical distribution
function for the q-deformed boson oscillators and develop an approximate theory
incorporating the zero-point energy. We are then able to demonstrate that for
small deformations, the theory reproduces the correct limits both for very high
temperatures and for very low temperatures. The deformed theory thus reduces to
the undeformed theory in these extreme cases.
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quant-ph
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Passivity and practical work extraction using Gaussian operations: Quantum states that can yield work in a cyclical Hamiltonian process form one
of the primary resources in the context of quantum thermodynamics. Conversely,
states whose average energy cannot be lowered by unitary transformations are
called passive. However, while work may be extracted from non-passive states
using arbitrary unitaries, the latter may be hard to realize in practice. It is
therefore pertinent to consider the passivity of states under restricted
classes of operations that can be feasibly implemented. Here, we ask how
restrictive the class of Gaussian unitaries is for the task of work extraction.
We investigate the notion of Gaussian passivity, that is, we present necessary
and sufficient criteria identifying all states whose energy cannot be lowered
by Gaussian unitaries. For all other states we give a prescription for the
Gaussian operations that extract the maximal amount of energy. Finally, we show
that the gap between passivity and Gaussian passivity is maximal, i.e.,
Gaussian-passive states may still have a maximal amount of energy that is
extractable by arbitrary unitaries, even under entropy constraints.
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quant-ph
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Equilibration of Quantum Gases: Finding equilibration times is a major unsolved problem in physics with few
analytical results. Here we look at equilibration times for quantum gases of
bosons and fermions in the regime of negligibly weak interactions, a setting
which not only includes paradigmatic systems such as gases confined to boxes,
but also Luttinger liquids and the free superfluid Hubbard model. To do this,
we focus on two classes of measurements: (i) coarse-grained observables, such
as the number of particles in a region of space, and (ii) few-mode
measurements, such as phase correlators and correlation functions. We show
that, in this setting, equilibration occurs quite generally despite the fact
that the particles are not interacting. Furthermore, for coarse-grained
measurements the timescale is generally at most polynomial in the number of
particles N, which is much faster than previous general upper bounds, which
were exponential in N. For local measurements on lattice systems, the timescale
is typically linear in the number of lattice sites. In fact, for one
dimensional lattices, the scaling is generally linear in the length of the
lattice, which is optimal. Additionally, we look at a few specific examples,
one of which consists of N fermions initially confined on one side of a
partition in a box. The partition is removed and the fermions equilibrate
extremely quickly in time O(1/N).
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quant-ph
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Experimental Quantum Error Correction: Quantum error correction is required to compensate for the fragility of the
state of a quantum computer. We report the first experimental implementations
of quantum error correction and confirm the expected state stabilization. In
NMR computing, however, a net improvement in the signal-to-noise would require
very high polarization. The experiment implemented the 3-bit code for phase
errors in liquid state state NMR.
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quant-ph
|
Retrodictive quantum state engineering: This thesis is concerned with retrodiction and measurement in quantum optics.
The latter of these two concepts is studied in particular form with a general
optical multiport device, consisting of an arbitrary array of beam-splitters
and phase-shifters. I show how such an apparatus generalizes the original
projection synthesis technique, introduced as an in principle technique to
measure the canonical phase distribution. Just as for the original projection
synthesis, it is found that such a generalised device can synthesize any
general projection onto a state in a finite dimensional Hilbert space. One of
the important findings of this thesis is that, unlike the original projection
synthesis technique, the general apparatus described here only requires a
classical, that is a coherent, reference field at the input of the device. Such
an apparatus lends itself much more readily to practical implementation and
would find applications in measurement and predictive state engineering.
If we relax the above condition to allow for just a single non-classical
reference field, we show that the apparatus is capable of producing a
single-shot measure of canonical phase. That is, the apparatus can project onto
any one of an arbitrarily large subset of phase eigenstates, with a probability
proportional to the overlap of the phase state and the input field. Unlike the
original projection synthesis proposal, this proposal requires a binomial
reference state as opposed to a reciprocal binomial state. We find that such a
reference state can be obtained, to an excellent approximation, from a suitably
squeezed state.
The analysis of these measurement apparatuses is performed in the less usual,
but completely rigorous, retrodictive formalism of quantum mechanics.
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quant-ph
|
A probabilistic approach to quantum Bayesian games of incomplete
information: A Bayesian game is a game of incomplete information in which the rules of the
game are not fully known to all players. We consider the Bayesian game of
Battle of Sexes that has several Bayesian Nash equilibria and investigate its
outcome when the underlying probability set is obtained from generalized
Einstein-Podolsky-Rosen experiments. We find that this probability set, which
may become non-factorizable, results in a unique Bayesian Nash equilibrium of
the game.
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quant-ph
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Comments on "Disproof of Bell's theorem": In a series of very interesting papers [1-7], Joy Christian constructed a
counterexample to Bell's theorem. This counterexample does not have the same
assumptions as the original Bell's theorem, and therefore it does not represent
a genuine disproof in a strict mathematical sense. However, assuming the
physical relevance of the new assumptions, the counterexample is shown to be a
contextual hidden variable theory. If Bell's theorem's importance is to rule
out contextual hidden variable theories obeying relativistic locality, then Joy
Christian's counterexample achieves its aim. If however contextual hidden
variables theories are not considered genuine physically theories and Bell's
theorem's importance stems from its ability to be experimentally confirmed,
then Joy Christian's counterexample does not diminish the importance of Bell's
theorem. The implications of Joy Christian's counterexample are discussed in
the context of information theory.
Version 2 note: Subsequent analysis disproved the mathematical consistency of
Joy Christian's model. This paper was based on the assumption of the
mathematical validity of the model. Except for the addition of this note, the
content of this paper was not modified in any other way.
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quant-ph
|
Deploying hybrid quantum-secured infrastructure for applications: When
quantum and post-quantum can work together: Most currently used cryptographic tools for protecting data are based on
certain computational assumptions, which makes them vulnerable with respect to
technological and algorithmic developments, such as quantum computing. One
existing option to counter this potential threat is quantum key distribution,
whose security is based on the laws of quantum physics. Quantum key
distribution is secure against unforeseen technological developments. A second
approach is post-quantum cryptography, which is a set of cryptographic
primitives that are believed to be secure even against attacks with both
classical and quantum computing technologies. From this perspective, this study
reviews recent progress in the deployment of the quantum-secured infrastructure
based on quantum key distribution, post-quantum cryptography, and their
combinations. Various directions in the further development of the full-stack
quantum-secured infrastructure are also indicated. Distributed applications,
such as blockchains and distributed ledgers, are also discussed.
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quant-ph
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Einstein-Podolsky-Rosen steering and Bell nonlocality of two macroscopic
mechanical oscillators in optomechanical systems: We investigate under which conditions quantum nonlocal manifestations as
Einstein-Podolsky-Rosen steering or Bell nonlocality can manifest themselves
even at the macroscopic level of two mechanical resonators in optomechanical
systems. We adopt the powerful scheme of reservoir engineering, implemented by
driving a cavity mode with a properly chosen two-tone field, to prepare two
mechanical oscillators into an entangled state. We show that large and robust
(both one-way and two-way) steering could be achieved in the steady state with
realistic parameters. We analyze the mechanism of the asymmetric nature of
steering in our system of two-mode Gaussian state. However, unlike steering,
Bell nonlocality is present under much more stringent conditions. We consider
two types of measurements, displaced parity and on-off detection, respectively.
We show that for both the measurements Bell violation requires very low
environmental temperature. For the parity detection, large Bell violation is
observed only in the transient state when the mechanical modes decouple from
the optical mode and with extremely small cavity losses and mechanical damping.
Whereas for the on-off detection, moderate Bell violation is found in the
steady state and robust against cavity losses and mechanical damping. Although
Bell violation with the parity detection seems extremely challenging to be
experimentally demonstrated, the conditions required for violating Bell
inequalities with the on-off detection are much less demanding.
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quant-ph
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Probing quantum floating phases in Rydberg atom arrays: The floating phase, a critical incommensurate phase, has been theoretically
predicted as a potential intermediate phase between crystalline ordered and
disordered phases. In this study, we investigate the different quantum phases
that arise in ladder arrays comprising up to 92 neutral-atom qubits and
experimentally observe the emergence of the quantum floating phase. We analyze
the site-resolved Rydberg state densities and the distribution of state
occurrences. The site-resolved measurement reveals the formation of domain
walls within the commensurate ordered phase, which subsequently proliferate and
give rise to the floating phase with incommensurate quasi-long-range order. By
analyzing the Fourier spectra of the Rydberg density-density correlations, we
observe clear signatures of the incommensurate wave order of the floating
phase. Furthermore, as the experimental system sizes increase, we show that the
wave vectors approach a continuum of values incommensurate with the lattice.
Our work motivates future studies to further explore the nature of
commensurate-incommensurate phase transitions and their non-equilibrium
physics.
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quant-ph
|
Determination of When an Outcome is Actualised in a Quantum Measurement
using DNA - Photolyase System: The biochemical attachment of photolyase to ultraviolet (uv) absorbed DNA
molecules provides a method for registering whether a source has emitted
photons. Here using laws of chemical kinetics and related experimental methods
we argue that the instant after which this information becomes discernible can
be empirically determined by retrodicting from relevant data when the
photolyase binding to uv-absorbed DNA molecules has started occuring. Thus an
empirically investigable twist is provided to the quantum measurement problem.
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quant-ph
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Quantum Radon Transform and Its Application: This paper extends the Radon transform, a classical image processing tool for
fast tomography and denoising, to the quantum computing platform. A new kind of
periodic discrete Radon transform (PDRT), called quantum Radon transform (QRT),
is proposed. The QRT has a quantum implementation that is exponentially faster
than the classical Radon transform. Based on the QRT, we design an efficient
quantum image denoising algorithm. The simulation results show that QRT
preserves the good denoising capability as in the classical PDRT. Also, a
quantum algorithm for interpolation-based discrete Radon transform (IDRT) is
proposed, which can be used for fast line detection. Both the quantum extension
of IDRT and the line detection algorithm can provide polynomial speedups over
the classical counterparts.
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quant-ph
|
Quantum mixing of Markov chains for special distributions: The preparation of the stationary distribution of irreducible,
time-reversible Markov chains is a fundamental building block in many heuristic
approaches to algorithmically hard problems. It has been conjectured that
quantum analogs of classical mixing processes may offer a generic quadratic
speed-up in realizing such stationary distributions. Such a speed-up would also
imply a speed-up of a broad family of heuristic algorithms.
However, a true quadratic speed up has thus far only been demonstrated for
special classes of Markov chains. These results often presuppose a regular
structure of the underlying graph of the Markov chain, and also a regularity in
the transition probabilities.
In this work, we demonstrate a true quadratic speed-up for a class of Markov
chains where the restriction is only on the form of the stationary
distribution, rather than directly on the Markov chain structure itself. In
particular, we show efficient mixing can be achieved when it is beforehand
known that the distribution is monotonically decreasing relative to a known
order on the state space. Following this, we show that our approach extends to
a wider class of distributions, where only a fraction of the shape of the
distribution is known to be monotonic. Our approach is built on the
Szegedy-type quantization of transition operators.
|
quant-ph
|
Spectral diffusion of phosphorus donors in silicon at high magnetic
field: We characterize the phase memory time of phosphorus donor electron spins in
lightly-doped natural silicon at high magnetic field (8.58 T) in the dark and
under low-power optical excitation. The spin echo decays are dominated by
spectral diffusion due to the presence of the 4.7% abundant spin-1/2 silicon-29
nuclei. At 4.2 K, the spectral diffusion time (T$_{SD}$) measured in the dark
is $124 \pm 7$ $\mu$s, a factor of 2 smaller than that measured at low magnetic
fields (0.35 T). Using a tunable laser we also measured the echo decay as the
wavelength of the optical excitation is swept across the band edge from 1050 nm
to 1090 nm. Above-bandgap optical excitation is seen to increase the spectral
diffusion time of the donor electron spin to $201 \pm 11$ $\mu$s. The physical
mechanism underlying both the decrease of T$_{SD}$ at high field and the
subsequent increase under optical excitation remains unclear.
|
quant-ph
|
Correlated photon-pair generation in reverse-proton-exchange PPLN
waveguides with integrated mode demultiplexer at 10 GHz clock: We report 10-ps correlated photon pair generation in periodically-poled
reverse-proton-exchange lithium niobate waveguides with integrated mode
demultiplexer at a wavelength of 1.5-um and a clock of 10 GHz. Using
superconducting single photon detectors, we observed a coincidence to
accidental count ratio (CAR) as high as 4000. The developed photon-pair source
may find broad application in quantum information systems as well as quantum
entanglement experiments.
|
quant-ph
|
Entropic uncertainty relations for Markovian and non-Markovian processes
under a structured bosonic reservoir: The uncertainty relation is a fundamental limit in quantum mechanics and is
of great importance to quantum information processing as it relates to quantum
precision measurement. Due to interactions with the surrounding environment, a
quantum system will unavoidably suffer from decoherence. Here, we investigate
the dynamic behaviors of the entropic uncertainty relation of an atom-cavity
interacting system under a bosonic reservoir during the crossover between
Markovian and non-Markovian regimes. Specifically, we explore the dynamic
behavior of the entropic uncertainty relation for a pair of incompatible
observables under the reservoir-induced atomic decay effect both with and
without quantum memory. We find that the uncertainty dramatically depends on
both the atom-cavity and the cavity-reservoir interactions, as well as the
correlation time, $\tau$, of the structured reservoir. Furthermore, we verify
that the uncertainty is anti-correlated with the purity of the state of the
observed qubit-system. We also propose a remarkably simple and efficient way to
reduce the uncertainty by utilizing quantum weak measurement reversal.
Therefore our work offers a new insight into the uncertainty dynamics for
multi-component measurements within an open system, and is thus important for
quantum precision measurements.
|
quant-ph
|
Presence of negative entropies in Casimir interactions: Negative entropy in connection with the Casimir effect at uniform temperature
is a phenomenon rooted in the circumstance that one is describing a nonclosed
system, or only part of a closed system. In this paper we show that the
phenomenon is not necessarily restricted to electromagnetic theory, but can be
derived from the quantum theory of interacting harmonic oscillators, most
typically two oscillators interacting not directly but indirectly via a third
one. There are two such models, actually analogous to the transverse magnetic
(TM) and transverse electric (TE) modes in electrodynamics. These mechanical
models in their simplest version were presented some years ago, by J. S.
H{\o}ye et al., Physical Review E {\bf 67}, 056116 (2003). In the present paper
we re-emphasize the physical significance of the mechanical picture, and extend
the theory so as to include the case where there are several mediating
oscillators, instead of only one. The TE oscillator exhibits negative entropy.
Finally, we show explicitly how the interactions via the electromagnetic field
contain the two oscillator models.
|
quant-ph
|
Resonance interaction of two entangled atoms accelerating between two
mirrors: We study the resonance interaction between two entangled identical atoms
coupled to a quantized scalar field vacuum, and accelerating between two
mirrors. We show how radiative processes of the two-atom entangled state can be
manipulated by the atomic configuration undergoing noninertial motion.
Incorporating the Heisenberg picture with symmetric operator ordering, the
vacuum fluctuation and the self-reaction contributions are distinguished. We
evaluate the resonance energy shift and the relaxation rate of energy of the
two atom system from the self-reaction contribution in the Heisenberg equation
of motion. We investigate the variation of these two quantities with relevant
parameters such as atomic acceleration, interatomic distance and position with
respect to the boundaries. We show that both the energy level shift and the
relaxation rate can be controlled by tuning the above parameters.
|
quant-ph
|
Simulating sparse Hamiltonians with star decompositions: We present an efficient algorithm for simulating the time evolution due to a
sparse Hamiltonian. In terms of the maximum degree d and dimension N of the
space on which the Hamiltonian H acts for time t, this algorithm uses
(d^2(d+log* N)||Ht||)^{1+o(1)} queries. This improves the complexity of the
sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders,
which scales like (d^4(log* N)||Ht||)^{1+o(1)}. To achieve this, we decompose a
general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of
non-zero entries have the property that every connected component is a star,
and efficiently simulate each of these pieces.
|
quant-ph
|
Remarks on the Relativistic Transactional Interpretation of Quantum
Mechanics: Kastner (arXiv:1709.09367) and Kastner and Cramer (arXiv:1711.04501) argue
that the Relativistic Transactional Interpretation (RTI) of quantum mechanics
provides a clear definition of absorbers and a solution to the measurement
problem. I briefly examine how RTI stands with respect to unitarity in quantum
mechanics. I then argue that a specific proposal to locate the origin of
nonunitarity is flawed, at least in its present form.
|
quant-ph
|
Understanding the Frauchiger-Renner Argument: In 2018, Daniela Frauchiger and Renato Renner published an article in Nature
Communications entitled `Quantum theory cannot consistently describe the use of
itself.' I clarify the significance of the result and point out a common and
persistent misunderstanding of the argument, which has been attacked as flawed
from a variety of interpretational perspectives.
|
quant-ph
|
Quantum characterization of bipartite Gaussian states: Gaussian bipartite states are basic tools for the realization of quantum
information protocols with continuous variables. Their complete
characterization is obtained by the reconstruction of the corresponding
covariance matrix. Here we describe in details and experimentally demonstrate a
robust and reliable method to fully characterize bipartite optical Gaussian
states by means of a single homodyne detector. We have successfully applied our
method to the bipartite states generated by a sub-threshold type-II optical
parametric oscillator which produces a pair of thermal cross-polarized
entangled CW frequency degenerate beams. The method provide a reliable
reconstruction of the covariance matrix and allows to retrieve all the physical
information about the state under investigation. These includes observable
quantities, as energy and squeezing, as well as non observable ones as purity,
entropy and entanglement. Our procedure also includes advanced tests for
Gaussianity of the state and, overall, represents a powerful tool to study
bipartite Gaussian state from the generation stage to the detection one.
|
quant-ph
|
Non-Markovian Open Quantum Systems: Lorentzian from Markovian: As a general mission, reduced dynamics and master equations are advocated as
alternative method and philosophy instead of Green functions, Kubo theory and
the like. A smart reduction of the Lorentzian open system to the Markovian one
(Imamoglu, 1994) is presented in simple terms.
|
quant-ph
|
Emergent universality in critical quantum spin chains: entanglement
Virasoro algebra: Entanglement entropy and entanglement spectrum have been widely used to
characterize quantum entanglement in extended many-body systems. Given a pure
state of the system and a division into regions $A$ and $B$, they can be
obtained in terms of the $Schmidt~ values$, or eigenvalues $\lambda_{\alpha}$
of the reduced density matrix $\rho_A$ for region $A$. In this paper we draw
attention instead to the $Schmidt~ vectors$, or eigenvectors
$|v_{\alpha}\rangle$ of $\rho_A$. We consider the ground state of critical
quantum spin chains whose low energy/long distance physics is described by an
emergent conformal field theory (CFT). We show that the Schmidt vectors
$|v_{\alpha}\rangle$ display an emergent universal structure, corresponding to
a realization of the Virasoro algebra of a boundary CFT (a chiral version of
the original CFT). Indeed, we build weighted sums $H_n$ of the lattice
Hamiltonian density $h_{j,j+1}$ over region $A$ and show that the matrix
elements $\langle v_{\alpha}H_n |v_{\alpha'}\rangle$ are universal, up to
finite-size corrections. More concretely, these matrix elements are given by an
analogous expression for $H_n^{\tiny \text{CFT}} = \frac 1 2 (L_n + L_{-n})$ in
the boundary CFT, where $L_n$'s are (one copy of) the Virasoro generators. We
numerically confirm our results using the critical Ising quantum spin chain and
other (free-fermion equivalent) models.
|
quant-ph
|
Comment on ``Validity of Feynman's prescription of disregarding the
Pauli principle in intermediate states'': In a recent paper Coutinho, Nogami and Tomio [Phys. Rev. A 59, 2624 (1999);
quant-ph/9812073] presented an example in which, they claim, Feynman's
prescription of disregarding the Pauli principle in intermediate states of
perturbation theory fails. We show that, contrary to their claim, Feynman's
prescription is consistent with the exact solution of their example.
|
quant-ph
|
Distances between quantum states in the tomographic-probability
representation: Distances between quantum states are reviewed within the framework of the
tomographic-probability representation. Tomographic approach is based on
observed probabilities and is straightforward for data processing. Different
states are distinguished by comparing corresponding probability-distribution
functions. Fidelity as well as other distance measures are expressed in terms
of tomograms.
|
quant-ph
|
Classical capacity of quantum non-Gaussian attenuator and amplifier
channels: We consider a quantum bosonic channel that couples the input mode via a beam
splitter or two-mode squeezer to an environmental mode that is prepared in an
arbitrary state. We investigate the classical capacity of this channel, which
we call a non-Gaussian attenuator or amplifier channel. If the environment
state is thermal, we of course recover a Gaussian phase-covariant channel whose
classical capacity is well known. Otherwise, we derive both a lower and an
upper bound to the classical capacity of the channel, drawing inspiration from
the classical treatment of the capacity of non-Gaussian additive-noise
channels. We show that the lower bound to the capacity is always achievable and
give examples where the non-Gaussianity of the channel can be exploited so that
the communication rate beats the capacity of the Gaussian-equivalent channel
(i.e., the channel where the environment state is replaced by a Gaussian state
with the same covariance matrix). Finally, our upper bound leads us to
formulate and investigate conjectures on the input state that minimizes the
output entropy of non-Gaussian attenuator or amplifier channels. Solving these
conjectures would be a main step towards accessing the capacity of a large
class of non-Gaussian bosonic channels.
|
quant-ph
|
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