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We study the measure theory of a two-site quantum random walk. The truncated decoherence functional defines a quantum measure $\mu_n$ on the space of $n$-paths, and the $\mu_n$ in turn induce a quantum measure $\mu$ on the cylinder sets within the space $\Omega$ of untruncated paths. |
Attempts to apply quantum collapse theories to Cosmology and cosmic inflation are reviewed. These attempts are motivated by the fact that the theory of cosmological perturbations of quantum-mechanical origin suffers from the single outcome problem, which is a modern incarnation of the quantum measurement problem, and ... |
The time evolution of the trace distance between two states of an open quantum system may increase due to initial system-environment correlations, thus exhibiting a breakdown of distance contractivity of the reduced dynamics. We analyze how the time evolution of the distance depends on the chosen distance measure. |
We present a method for the direct measurement of the Wigner characteristic function of a thermalizing harmonic oscillator that is completely inaccessible for control or measurement. The strategy employs a recently proposed probe-measurement-based scheme [Phys. Rev. Lett. 122, 110406 (2019)] which relies on the pulsed... |
We study the decay dynamics of a two-level giant atom that is coupled to a waveguide with time-dependent coupling strengths. In the non-Markovian regime where the retardation effect cannot be ignored, we show that the dynamics of the atom depends on the atom-waveguide coupling strengths at an earlier time. |
We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing machine. This model is based on the extension of von Neumann's quan... |
We propose and analyze a mechanism for Bose-Einstein condensation of stationary dark-state polaritons. Dark-state polaritons (DSPs) are formed in the interaction of light with laser-driven 3-level Lambda-type atoms and are the basis of phenomena such as electromagnetically induced transparency (EIT), ultra-slow and st... |
Linear optical multiports are widely used in photonic quantum information processing. Naturally, these devices are directionally-biased since photons always propagate from the input ports toward the output ports. |
Quantum signal processing (QSP) is a methodology for constructing polynomial transformations of a linear operator encoded in a unitary. Applied to an encoding of a state $\rho$, QSP enables the evaluation of nonlinear functions of the form $\text{tr}(P(\rho))$ for a polynomial $P(x)$, which encompasses relevant proper... |
Recent breakthroughs have ushered the quantum network into a new era, where quantum information can be stored, transferred, and processed across multiple nodes on a metropolitan scale. A key challenge in this new era is enhancing the capabilities of individual nodes, providing precise and robust control over multiple ... |
We present a quantum augmented variant of the dual lattice attack on the Learning with Errors (LWE) problem, using classical memory with quantum random access (QRACM). Applying our results to lattice parameters from the literature, we find that our algorithm outperforms previous algorithms, assuming unit cost access t... |
We derive entropic inseparability criteria for the phase space representation of quantum states. In contrast to criteria involving differential entropies of marginal phase space distributions, our criteria are based on a joint distribution known as the Husimi Q-distribution. |
We consider Einstein-Podolsky-Rosen steering in the regime where the parties can perform collective measurements on many copies of a given shared entangled state. We derive a simple and efficient condition for guaranteeing that an entangled state is $k$-copy steerable. |
We slightly strengthen an operator inequality identified by Correggi et al. that lower bounds the energy of a Heisenberg-coupled graph of $s=1/2$ spins using the total spin. In particular, $\Delta H \ge C \Delta\vec{S}^2$ for a graph-dependent constant $C$, where $\Delta H$ is the energy above the ground state and $\D... |
Quantum computers are projected to handle the Gibbs sampling and the related inference on Markov networks effectively. Apart from noting the background information useful for those starting the explorations in this important thread of Quantum Machine Learning, we capture some results and observations obtained through ... |
Using a quantum theory for an ensemble of three-level atoms (lambda) placed in an optical cavity abd driven by electromagnetic fields, we show that the long-lived spin associated with the ground state sublevels can be squeezed. Two kinds of squeezing are obtained: self-spin squeezing, when the input fields are coheren... |
The optical phase of the driving field in the process of high harmonic generation and the coherence properties of the harmonics are fundamental concepts in attosecond physics. Here, we consider to drive the process by incoherent classical and non-classical light fields exhibiting an undetermined optical phase. |
p-Adic quantum mechanics is constructed from the Dirac-von Neumann axioms identifying quantum states with square-integrable functions on the N-dimensional p-adic space. This choice is equivalent to the hypothesis of the discreteness of the space. |
This article reviews the history of digital computation, and investigates just how far the concept of computation can be taken. In particular, I address the question of whether the universe itself is in fact a giant computer, and if so, just what kind of computer it is. I will show that the universe can be regarded as... |
Non-Hermiticity enables macroscopic accumulation of bulk states, named non-Hermitian skin effects. The non-Hermitian skin effects are well-established for single-particle systems, but their proper characterization for general systems is elusive. |
A new aspect of understanding a Fano absorption spectrum is presented in terms of the complex spectral analysis. The absorption spectrum of an impurity embedded in semi-infinite superlattice is investigated. |
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round consisting of O(log(n)) bits. |
Typically, time-dependent thermodynamic protocols need to run asymptotically slowly in order to avoid dissipative losses. By adapting ideas from counter-diabatic driving and Floquet engineering to open systems, we develop fast-forward protocols for swiftly thermalizing a system oscillator locally coupled to an optical... |
For the electric polarizability of a bound system in relativistic quantum theory, there are two definitions that have appeared in the literature. They differ depending on whether or not the vacuum background is included in the system. |
We study the amplification of security against quantum attacks provided by iteration of block ciphers. In the classical case, the Meet-in-the-middle attack is a generic attack against those constructions. |
We highlight three conflicts between quantum theory and classical general relativity, which make it implausible that a quantum theory of gravity can be arrived at by quantising classical gravity. These conflicts are: quantum nonlocality and space-time structure; the problem of time in quantum theory; and the quantum m... |
In this paper we show the series of Greenberger-Horne-Zeilinger paradoxes for N maximally entangled N-dimensional quantum systems. |
The absorption of a single photon that excites a quantum system from a low to a high energy level is an elementary process of light-matter interaction, and a route towards realizing pure single-photon absorption has both fundamental and practical implications in quantum technology. Due to nonlinear optical effects, ho... |
Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum system, resulting in the coherent information and introduced here the compatible inf... |
We study the entanglement evolution of two coupled qubits in interaction with an external environment and in the presence of an external magnetic field with a stochastic component. The results show the expected degradation of entanglement due to the noise. |
Quantum networks are the center of many of the recent advances in quantum science, not only leading to the discovery of new properties in the foundations of quantum theory but also allowing for novel communication and cryptography protocols. It is known that networks beyond that in the paradigmatic Bell's theorem ... |
Following the evolution under a non-Hermitian Hamiltonian (nHH) involves significant probability loss. This makes various nHH effects impractical in the quantum realm. |
A modified weak measurement scheme, rotatory biased weak measurement, is proposed to significantly improve the sensitivity and resolution of the refractive index sensor on a total reflection structure. This method introduces an additional phase in the post-selected procedure and generates an extinction point in the sp... |
Qubit systems based on trapped ultracold ions win one of the leading positions in the quantum computing field, demonstrating quantum algorithms with the highest complexity to date. Surface Paul traps for ion confinement open the opportunity to scale quantum processors to hundreds of qubits and enable high-connectivity... |
Simultaneous measurement of several noncommuting observables is modeled by using semigroups of completely positive maps on an algebra with a non-trivial center. The resulting piecewise-deterministic dynamics leads to chaos and to nonlinear iterated function systems (quantum fractals) on complex projective spaces. |
It is challenging to construct metrology schemes which harness quantum features such as entanglement and coherence to surpass the standard quantum limit. We propose an ansatz for devising adaptive-feedback quantum metrology (AFQM) strategy which reduces greatly the searching space. |
We discuss error-correction properties for families of quantum low-density parity check (LDPC) codes with relative distance that tends to zero in the limit of large blocklength. In particular, we show that any family of LDPC codes, quantum or classical, where distance scales as a positive power of the block length, $d... |
Quantum key distribution (QKD) allows the establishment of common cryptographic keys among distant parties. Many of the QKD protocols that were introduced in the past involve the challenge of monitoring the signal disturbance over the communication line, in order to evaluate the information leakage to a potential eave... |
Randomly poled nonlinear crystals are shown to be able to emit intense ultra-broadband photon-pair fields with properties comparable to those coming from chirped periodically-poled crystals. Their intensities scale linearly with the number of domains. |
The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen-Cooper-Schrieffer (PBCS) wavefunction. It is also an elementary symmetric polynomial (ESP) state. |
In this work we show that in double-slit experiment properties incompatible with Which Slit property can be detected without erasing the knowledge of which slit each particle passes through and without affecting the point of impact on the final screen. A systematic procedure to find these particular properties is prov... |
Generalization of quantum information splitting protocol from qubits to qudits (quantum d-dimensional systems) is presented. |
Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital methods, such as lower systematic errors and reduced circuit depth, making them ... |
We present in an informal way some recent results concerning a possible overlapping between classical unpredictability and quantum indeterminism. |
In this paper, we explore how to constructively manipulate qubits by rotating Bloch spheres. It is revealed that three-rotation and one-rotation Hamiltonian controls can be constructed to steer qubits when two tunable Hamiltonian controls are available. |
We explore the feasibility of implementing a small surface code with 9 data qubits and 8 ancilla qubits, commonly referred to as surface-17, using a linear chain of 171Yb+ ions. Two-qubit gates can be performed between any two ions in the chain with gate time increasing linearly with ion distance. |
We review an event-based simulation approach which reproduces the statistical distributions of wave theory not by requiring the knowledge of the solution of the wave equation of the whole system but by generating detection events one-by-one according to an unknown distribution. We illustrate its applicability to vario... |
Dissipative tunneling remains a cornerstone effect in quantum mechanics. In chemistry, it plays a crucial role in governing the rates of chemical reactions, often modeled as the motion along the reaction coordinate from one potential well to another. |
The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors. The E(R) is positive below some threshold R', which implies R' is a low... |
We discuss stochastic resonance (SR) effects in driven coupled quantum systems. We construct dynamical and information theoretic measures of the system's response that exhibit a non-monotonic behaviour as a function of the noise strength. |
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is bounded from below. |
Nitrogen-Vacancy (NV) centers in diamond have been identified over the past few years as promising systems for a variety of applications, ranging from quantum information science to magnetic sensing. This relies on the unique optical and spin properties of the negatively charged NV. |
We consider an SU(1,1) interferometer employing four-wave mixers that is fed with two-mode states which are both coherent and intelligent states of the SU(1,1) Lie group. It is shown that the phase sensitivity of the interferometer can be essentially improved by using input states with a large photon-number difference... |
Whether one is interested in quantum state preparation or in the design of efficient heat engines, adiabatic (reversible) transformations play a pivotal role in minimizing computational complexity and energy losses. Understanding the structure of these transformations and identifying the systems for which such transfo... |
It is well known that no quantum error correcting code of rate $R$ can correct adversarial errors on more than a $(1-R)/4$ fraction of symbols. But what if we only require our codes to *approximately* recover the message? |
A general formulation of the problem of detection for a pair of two cones is presented. The special case is the detection of entangled states by entanglement witnesses. |
We study the role of quantum statistics in the self-ordering of ultracold bosons and fermions moving inside an optical resonator with transverse coherent pumping. For few particles we numerically compute the nonequilibrium dynamics of the density matrix towards the self-ordered stationary state of the coupled atom-cav... |
Electron channeling in silicon crystals has brought forward the possibility of having detected a particle's "internal clock", as an intrinsic oscillation with de Broglie's frequency. The transmission probability along a major axial direction is reduced with respect to neighboring angles, except for a s... |
We present a general scheme for implementing bi-directional quantum state transfer in a quantum swapping channel. Unlike many other schemes for quantum computation and communication, our method does not require qubit couplings to be switched on and off. |
One of the simplest security proofs of quantum key distribution is based on the so-called complementarity scenario, which involves the complementarity control of an actual protocol and a virtual protocol [M. Koashi, e-print <a href="https://arxiv.org/abs/0704.3661" data-arxiv-id="0704.3661" class="link-https">arXiv:070... |
We show that the Knill Laflamme Milburn method of quantum computation with linear optics gates can be interpreted as a one-way, measurement based quantum computation of the type introduced by Briegel and Rausendorf. We also show that the permanent state of n n-dimensional systems is a universal state for quantum compu... |
We establish several strong equivalences of synchronous non-local games, in the sense that the corresponding game algebras are $*$-isomorphic. We first show that the game algebra of any synchronous game on $n$ inputs and $k$ outputs is $*$-isomorphic to the game algebra of an associated bisynchronous game on $nk$ inpu... |
We probe the principle of complementarity by performing a double-slit experiment based on entangled photons created by spontaneous parametric down-conversion from a pump mode in a TEM01-mode. Our setup brings out the need for a careful selection of the signal-idler photon pairs for our study of visibility and distingu... |
We present a resource-performance tradeoff of an all-optical quantum repeater that uses photon sources, linear optics, photon detectors and classical feedforward at each repeater node, but no quantum memories. We show that the quantum-secure key rate has the form $R(\eta) = D\eta^s$ bits per mode, where $\eta$ is the ... |
We present a fully quantum model for the excitation of a bound electron based on the free-electron bound-electron resonant interaction (FEBERI) scheme. The bound electron is modeled as a quantum two-level system (TLS) at any initial quantum (qubit) state, and the free electron is presented as a pre-shaped quantum elec... |
Quantum illumination uses quantum correlations to enhance the detection of an object in the presence of background noise. This advantage has been shown to exist even if one uses non-optimal direct measurements on the two correlated modes. |
In two companion papers it was shown how to separate out from a scattering function in quantum electrodynamics a distinguished part that meets the correspondence-principle and pole-factorization requirements. The integrals that define the terms of the remainder are here shown to have singularities on the pertinent Lan... |
We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models as special cases. |
In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph, propagation between a particular pair of nodes is exponentially faster in the quantum ca... |
Quantum computing is emerging as a promising technology for solving complex optimization problems that arise in various engineering fields, and therefore has the potential to also significantly impact power electronics applications. This paper offers a concise tutorial on fundamental concepts in quantum computing, ser... |
Distributing quantum entanglement on a chip is a crucial step towards realizing scalable quantum processors. Using traveling phonons - quantized guided mechanical wavepackets - as a medium to transmit quantum states is currently gaining significant attention, due to their small size and low propagation speed compared ... |
There has been much recent interest in quantum optical interferometry for applications to metrology, sub-wavelength imaging, and remote sensing, such as in quantum laser radar (LADAR). For quantum LADAR, atmospheric absorption rapidly degrades any quantum state of light, so that for high-photon loss the optimal strate... |
Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair states (PEPS), then the set of tensor network states of given bond dimension is... |
The fundamental equations of particle motion lead to a modified Poisson equation including dynamic charge. This charge derives from density oscillations of a particle; it is not discrete, but continuous. |
Raman process is used for generation of nonclassical states and subsequent applications due to its simplicity. In view of the experimental feasibility of the off-resonant Raman process at single photon level useful in long distance quantum communication and quantum memory, we perform here a detailed study of possibili... |
In classical mechanics, a nonrelativistic particle constrained on an $N-1$ curved hypersurface embedded in $N$ flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of the geometric potential. |
Pulse-based quantum machine learning (QML) models possess full expressivity when they are ensemble controllable. However, it has also been shown that barren plateaus emerge in such models, rendering training intractable for systems with large dimension. |
Creating non-classical states of light from simple quantum systems together with classical resources is a challenging problem. We show how chiral emitters under a coherent drive can generate non-classical photon states. |
When tackling binary optimization problems using quantum algorithms, the conventional Ising representation and Quantum Approximate Optimization Algorithm (QAOA) encounter difficulties in efficiently handling errors for large-scale problems involving multiple constraints. To address these challenges, this paper present... |
The demonstration of optical multipath interference from a large number of quantum emitters is essential for the realization of many paradigmatic experiments in quantum optics. However, such interference remains still unexplored as it crucially depends on the sub-wavelength positioning accuracy and stability of all em... |
In the current noisy intermediate scale quantum computing era, and after the significant progress of the quantum hardware we have seen in the past few years, it is of high importance to understand how different quantum algorithms behave on different types of hardware. This includes whether or not they can be implement... |
Quanta splitting is an essential generator of Gaussian entanglement, exemplified by Einstein-Podolsky-Rosen states and apparently the most commonly occurring form of entanglement. In general, it results from the strong pumping of a nonlinear process with a highly coherent and low-noise external drive. |
Fluxonium qubit is a promising building block for quantum information processing due to its long coherence time and strong anharmonicity. In this paper, we realize a 60 ns direct CNOT-gate on two inductively-coupled fluxonium qubits using selective darkening approach, resulting in a gate fidelity as high as 99.94%. |
We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the information-theoretic paradigm, exhibit a universal behaviour. In particular, for Haar unifo... |
We describe a novel scheme to implement scalable quantum information processing using Li-Cs molecular state to entangle $^{6}$Li and $^{133}$Cs ultracold atoms held in independent optical lattices. The $^{6}$Li atoms will act as quantum bits to store information, and $^{133}$Cs atoms will serve as messenger bits that ... |
We introduce a formalism to solve the problem of photon scattering from a system of multi-level quantum emitters. Our approach provides a direct solution of the scattering dynamics. |
Four critical elementary mathematical mistakes in Joy Christian's counterexample to Bell's theorem are presented. Consequently, Joy Christian's hidden variable model cannot reproduce any quantum mechanics results and cannot be used as a counterexample to Bell's theorem. |
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architect... |
Quantum illumination is to discern the presence or absence of a low reflectivity target, where the error probability decays exponentially in the number of copies used. When the target reflectivity is small so that it is hard to distinguish target presence or absence, the exponential decay constant falls into a class o... |
We discuss a mechanical model which mimics the main features of the radiation matter interaction in the black body problem. The pure classical dynamical evolution, with a simple discretization of the action variables, leads to the Stefan- Boltzmann law and to the Planck distribution without any additional statistical ... |
We describe an experimentally realistic situation of the quantum reflection of helium atoms from an oscillating surface. The temporal modulation of the potential induces clear sidebands in the reflection probability as a function of momentum. |
$^{171}$Yb$^{3+}$-doped Y$_2$SiO$_5$ crystals are a promising platform for optical quantum memories in long-distance quantum communications. The relevance of this material lies in $^{171}$Yb long optical and spin coherence times, along with a large hyperfine splitting, enabling long quantum storage over large bandwidt... |
A quantum particle evolving by Schrödinger'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. |
Semiconductor microcavities with artificial single-photon emitters have become one of the backbones of semiconductor quantum optics. In many cases however, technical and physical issues limit the study of optical fields to incoherently excited systems. |
We address binary and quaternary communication channels based on correlated multiphoton two-mode states of radiation in the presence of losses. The protocol are based on photon number correlations and realized upon choosing a shared set of thresholds to convert the outcome of a joint photon number measurement into a s... |
In recent years, analysis and control of quantum chaos are increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. This research aims to connect Newton's world to the quantum world by the complex mechanics so that quantu... |
Models of quantum computation are important because they change the physical requirements for achieving universal quantum computation (QC). For example, one-way QC requires the preparation of an entangled "cluster" state followed by adaptive measurement on this state, a set of requirements which is different f... |
In this note, I highlight a useful formula for the SWAP operator as an average of anti-correlated Heisenberg-Weyl displacements, valid for arbitrary-dimensional quantum systems. As an application I show how the relation can be used to quickly prove normalization identities for the Weyl function, and apply the result t... |
Secure communication protocols are often formulated in a paradigm where the message is encoded in measurement outcomes. In this work we propose a rather unexplored framework in which the message is encoded in measurement settings rather than in their outcomes. |
The stationary solution \rho of a quantum master equation can be represented as an ensemble of pure states in a continuous infinity of ways. An ensemble which is physically realizable through monitoring the system's environment we call an `unraveling'. |
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