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Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important - more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its connections to non-integrability are under active investigation. In this work, we s...
Quantum computing is deemed to require error correction at scale to mitigate physical noise by reducing it to lower noise levels while operating on encoded logical qubits. Popular quantum error correction schemes include CSS code, of which surface codes provide regular mappings onto 2D planes suitable for contemporary...
Understanding and improving generalization capabilities is crucial for both classical and quantum machine learning (QML). Recent studies have revealed shortcomings in current generalization theories, particularly those relying on uniform bounds, across both classical and quantum settings.
We show that the authors of the commented paper draw their conclusions from the eigenvalues of truncated Hamiltonian matrices that do not converge as the matrix dimension increases. In one of the studied examples the authors missed the real positive eigenvalues that already converge towards the exact eigenvalues of th...
We review recent work on the foundations of thermodynamics in the light of quantum information theory. We adopt a resource-theoretic perspective, wherein thermodynamics is formulated as a theory of what agents can achieve under a particular restriction, namely, that the only state preparations and transformations that...
We suggest a novel optical parametric generator (OPG) in which one of the down-converted beams is spontaneously generated along the Poynting vector of the pump beam. In this configuration, the generation takes advantage of the walk-off of the extraordinary pump rather than being degraded by it.
We obtain photon statistics by using a quantum jump approach tailored to a system in which one or two qubits are coupled to a one-dimensional waveguide. Photons confined in the waveguide have strong interference effects, which are shown to play a vital role in quantum jumps and photon statistics.
The Fermi two-atom problem illustrates an apparent causality violation in Quantum Field Theory which has to do with the nature of the built in correlations in the vacuum. It has been a constant subject of theoretical debate and discussions during the last few decades.
Passive quantum key distribution (QKD) has been proposed for discrete variable protocols to eliminate side channels in the source. Unfortunately, the key rate of passive DV-QKD protocols suffers from sifting loss and additional quantum errors.
We analyse periodically modulated quantum systems with $SU(2)$ and $SU(1,1)$ symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant transitions emerging in time-dependent systems.
The collective interactions of nanoparticles arranged in periodic structures give rise to high-$Q$ in-plane diffractive modes known as surface lattice resonances (SLRs). While these resonances and their broader implications have been extensively studied within the framework of classical electrodynamics and linear resp...
Recent proposed ``loophole-free'' Bell tests are discussed in the light of classical models for the relevant features of optical parametric amplification and homodyne detection. The Bell tests themselves are uncontroversial: there are no obvious loopholes that might cause bias and hence, if the world does, aft...
Quantum cryptography allows confidential information to be communicated between two parties, with secrecy guaranteed by the laws of nature alone. However, upholding guaranteed secrecy over quantum communication networks poses a further challenge, as classical receive-and-resend routing nodes can only be used condition...
We have investigated the time-evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can be investigated analytically.
The oscillating magnetic field produced by unbalanced currents in radio-frequency ion traps induces transition frequency shifts and sideband transitions that can be harmful to precision spectroscopy experiments. Here, we describe a methodology, based on two-photon spectroscopy, for determining both the strength and di...
We propose a theoretical scheme to show the possibility of achieving the quantum ground state cooling of a vibrating micromechanical membrane inside a high finesse optical cavity by back-action cooling approach. The scheme is based on an intensity-dependent coupling of the membrane to the intracavity radiation pressur...
Exceptional points (EPs) are special points in non-Hermitian systems where both eigenvalues and eigenvectors coalesce. In open quantum systems, these points are typically analyzed using effective non-Hermitian Hamiltonians or Liouvillian superoperators.
One of the fundamental concepts of quantum information theory is that of entanglement purification; that is, the transformation of a partially entangled state into a smaller-dimensional, more completely entangled state. Of particular interest are protocols for entanglement purification (EPPs) that alternate purely loc...
In a series of recent works, an interesting quantum generative model based on parameterized instantaneous polynomial quantum (IQP) circuits has emerged as they can be trained efficiently classically using any loss function that depends only on the expectation values of observables of the model. The model is proven not...
Resource theories constitute a powerful theoretical framework and a tool that captures, in an abstract structure, pragmatic aspects of the most varied theories and processes. For physical theories, while this framework deals directly with questions about the concrete possibilities of carrying out tasks and processes, ...
Coherence is a basic notion for quantum states. Instead of quantum states, in this work, We establish a resource theory for quantifying the coherence of Gaussian channels.
Distributed quantum metrology (DQM) enables the estimation of global functions of d distributed parameters beyond the capability of separable sensors. Continuous-variable DQM involves using a linear network with at least one nonclassical input.
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 metho...
Non-classical multi-photon and number states attracts many people because of their wide applications in fundamental quantum mechanics tests, quantum metrology and quantum computation, therefore it is a longstanding aim to generate such states experimentally. Here, we prepare photon triplets by using the spontaneously ...
A new approximate Quantum State Preparation (QSP) method is introduced, called the Walsh Series Loader (WSL). The WSL approximates quantum states defined by real-valued functions of single real variables with a depth independent of the number $n$ of qubits.
Different from the previous works on generating entangled states, this work is focused on how to transfer the prepared entangled states onto memory qubits for protecting them against decoherence. We here consider a physical system consisting of $n$ operation qubits and $2n$ memory qubits placed in a cavity or coupled ...
The $d^2$ Pauli operators attached to a composite qudit in dimension $d$ may be mapped to the vectors of the symplectic module $\mathcal{Z}_d^{2}$ ($\mathcal{Z}_d$ the modular ring). As a result, perpendicular vectors correspond to commuting operators, a free cyclic submodule to a maximal commuting set, and disjoint s...
A very simple illustration of the Bell-Kochen-Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the \emph{existence} of putative values for position and momentum observables for one single particle is incompatible with quantum mech...
We propose a method for learning temporal data using a parametrized quantum circuit. We use the circuit that has a similar structure as the recurrent neural network which is one of the standard approaches employed for this type of machine learning task.
In a recent Letter, Bennett and coworkers [1] argue that proofs of exotic quantum effects using closed timelike curves (CTC's) based on the work of Deutsch [2], or other nonlinear quantum dynamics, suffer from a fallacy that they call the "linearity trap," by which one cannot assume that a classical mixture...
The ground-state entanglement of a single particle of the N-harmonium system (i.e., a completely-integrable model of $N$ particles where both the confinement and the two-particle interaction are harmonic) is shown to be analytically determined in terms of $N$ and the relative interaction strength. For bosons, we compu...
Probing the real time dynamics of a reacting molecule remains one of the central challenges in chemistry. In this letter we show how the time-dependent wavefunction of an excited-state reacting molecule can be completely reconstructed from resonant coherent anti-Stokes Raman spectroscopy.
We discuss quantum dynamics in multi-dimensional non-linear systems. It is well-known that wave functions are localized in a kicked rotor model.
Matsumoto and Amano (2008) showed that every single-qubit Clifford+T operator can be uniquely written of a particular form, which we call the Matsumoto-Amano normal form. In this mostly expository paper, we give a detailed and streamlined presentation of Matsumoto and Amano's results, simplifying some proofs along...
The influence of outside quantum noises on the amplification of weak measurements is investigated. Three typical quantum noises are discussed.
The scaling law of entanglement entropy could undergo qualitative changes during the nonunitary evolution of a quantum many-body system. In this work, we uncover such entanglement phase transitions in one-dimensional non-Hermitian quasicrystals (NHQCs).
We describe a simple scheme for calculating the fidelity of a composite pulse when considered as a universal rotor.
The gauge symmetry is one of the most important concepts in modern physics, but there are two conflicting views on its meaning or interpretation. The standard view is that local gauge symmetry is the basis of the pursue of fundamental particles and forces in nature.
The quest of this work is to present discussions of some fundamental questions of economics in the era of quantum technology, which require a treatment different from economics studied thus far in the literature. A study of quantum economic behavior will become the center of attention of economists in the coming decad...
The probabilistic structure of quantum mechanics is investigated in the frequency framework. Such an approach can be interpreted as a contextual approach to quantum probabilities.
The coherence properties of mechanical resonators are often limited by multiple unavoidable forms of loss -- including phonon-phonon and phonon-defect scattering -- which result in the scattering of sound into other resonant modes and into the phonon bath. Dynamic suppression of this scattering loss can lift constrain...
The continuous pumping of atoms into a Bose-Einstein condensate via spontaneous emission from a thermal reservoir is analyzed. We consider the case of atoms with a three-level $\Lambda$ scheme, in which one of the atomic transitions has a very much shorter life-time than the other one.
Classical dynamical systems close to a critical point are known to act as efficient sensors due to a strongly nonlinear response. We explore such systems in the quantum regime by modeling a quantum version of a driven van der Pol oscillator.
We investigate a quantum many-body system with particles moving on a circle and subject to two-body and three-body potentials. In this new class of models, that extrapolates from the celebrated Calogero-Sutherland model and a system with interactions among nearest and next-to-nearest neighbors, the interactions can be...
The following paper provides a protocol to physically generate a $2$-qutrit entangling gate in the Kauffman-Jones version of $SU(2)$ Chern-Simons theory at level $4$. The protocol uses elementary operations on anyons consisting of braids, interferometric measurements, fusions and unfusions and ancilla pair creation.
Following the first paper on quantum algorithms for SDP-solving by Brandão and Svore in 2016, rapid developments has been made on quantum optimization algorithms. Recently Brandão et al. improved the quantum SDP-solver in the so-called quantum state input model, where the input matrices of the SDP are given as purifie...
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics.
Solving short and long time dynamics of closed quantum many-body systems is one of the main challenges of both atomic and condensed matter physics. For locally interacting closed systems, the dynamics of local observables can always be expanded into (pseudolocal) eigenmodes of the Liouvillian, so called dynamical symm...
Quantum mechanics is an extremely successful theory that agrees with every experiment. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are never found in a linear superposition of position states.
Spin interaction Hamiltonians are obtained from the unitary Yang--Baxter $\breve{R}$-matrix. Based on which, we study Berry phase and quantum criticality in the Yang--Baxter systems.
We consider a discrete-time 2-state quantum walk on the line. The state of the quantum walker evolves according to a rule which is determined by a coin-flip operator and a position-shift operator.
Specific quantum phase transitions of our interest are assumed associated with the fall of a closed, unitary quantum system into its exceptional-point (EP) singularity. The physical realization of such a "quantum catastrophe" (connected, typically, with an instantaneous loss of the diagonalizability of the cor...
A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.
Interferometric complementarity is known to be one of the most nonclassical manifestations of the quantum formalism. It is commonly known as wave-particle duality and has been studied presently from the perspective of quantum information theory where wave and particle nature of a quantum system, called quanton, are ch...
The integration of photonic components into surface ion traps provides a scalable approach for trapped-ion quantum computing, sensing, and metrology, enabling compact systems with enhanced stability and precision. However, the introduction of optical apertures in the trap electrodes can distort the trapping electric f...
An ideal and reversible transfer technique for the quantum state between light and metastable collective states of matter is presented and analyzed in detail. The method is based on the control of photon propagation in coherently driven 3-level atomic media, in which the group velocity is adiabatically reduced to zero...
The problem of photon adding and subtracting is studied, using conditional output measurement on a beam splitter. It is shown that for various classes of states the corresponding photon-added and -subtracted states can be prepared.
Many-body fermionic quantum calculations performed on analog quantum computers are restricted by the presence of k-local terms, which represent interactions among more than two qubits. These originate from the fermion-to-qubit mapping applied to the electronic Hamiltonians.
Unconditionally secure two-party bit commitment based solely on the principles of quantum mechanics (without exploiting special relativistic signalling constraints, or principles of general relativity or thermodynamics) has been shown to be impossible, but the claim is repeatedly challenged. The quantum bit commitment...
We present a new analysis of the connection between the classical conservation theorems and the role played by the Dirac matrices in order to obtain a four spinor version of the Dirac equation for the two electrons bound problem. The separation of the set of equations in its angular and radial parts is done and an asy...
Although the quality of quantum bits (qubits) and quantum gates has been steadily improving, the available quantity of qubits has increased quite slowly. To address this important issue in quantum computing, we have demonstrated arbitrary single qubit gates based on targeted phase shifts, an approach that can be appli...
Relativistically, time $t$ is an observable just like position $r$. In quantum theory, $t$ is a parameter, in contrast to the observable $r$.
While quantum circuits built from two-particle dual-unitary (maximally entangled) operators serve as minimal models of typically nonintegrable many-body systems, the construction and characterization of dual-unitary operators themselves are only partially understood. A nonlinear map on the space of unitary operators w...
By associating a binary signal with the relativistic worldline of a particle, a binary form of the phase of non-relativistic wavefunctions is naturally produced by time dilation. An analog of superposition also appears as a Lorentz filtering process, removing paths that are relativistically inequivalent.
It is believed that the more we have {\it a priori} information on input states, the better we can make the quality of clones in quantum cloning machines. This common sense idea was confirmed several years ago by analyzing a situation, where the input state is either one of two non-orthogonal states.
Maximally entangled photon pairs with a spatial degree of freedom is a potential way for realizing high-capacity quantum computing and communication. However, methods to generate such entangled states with high quality, high brightness, and good controllability are needed.
Dicke superradiance describes the collective radiative decay of a fully inverted ensemble of two-level atoms. We experimentally investigate this effect for a chiral, i.e.,~direction-dependent light--matter coupling.
A disagreement of the empirical results with quantum mechanical predictions is pointed out in the experiment by B. G. Christensen et al. The anomaly is quite similar to one present in the analogous experiment by M. Giustina et al.
Although it is impossible for a bit commitment protocol to be both arbitrarily concealing and arbitrarily binding, it is possible for it to be both partially concealing and partially binding. This means that Bob cannot, prior to the beginning of the unveiling phase, find out everything about the bit committed, and Ali...
A fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel, the probability of correctly decoding goes to zero exponentially in the number of channel uses, even when we allow code states which are entangled across several uses ...
Time-reversal ($\mathcal{T}$-) symmetry is fundamental to many physical processes. Typically, $\mathcal{T}$-breaking for microscopic processes requires the presence of magnetic field.
In this paper we discuss the traditional approaches to the problem of the arrow of time. On the basis of this discussion we adopt a global and non-entropic approach, according to which the arrow of time has a global origin and is an intrinsic, geometrical feature of space-time.
To implement fault-tolerant quantum computation (FTQC) with continuous variables, continuous variables need to be digitized using an appropriate code such as the Gottesman--Kitaev--Preskill (GKP) qubit. The scheme introduced in [K. Fukui et. al., Phys. Rev. X 8, 021054 (2018)] has reduced the threshold of a squeezing ...
We report an algorithm designed to perform computer-automated tuning of a single quantum dot with a charge sensor. The algorithm performs an adaptive measurement sequence of sub-sized stability diagrams until the single-electron regime is identified and reached.
We study the properties of sequences of the energy eigenvalues for some generalizations of q-deformed oscillators including the p,q-oscillator, the 3-, 4- and 5-parameter deformed oscillators given in the literature. It is shown that most of the considered models belong to the class of so-called Fibonacci oscillators ...
The Travelling Salesman Problem (TSP) is an important combinatorial optimisation problem, and is usually solved on a quantum computer using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation or a Higher Order Binary Optimisation(HOBO) formulation. In these formulations, penalty terms are added to the obj...
Attenuating a quantum state using a beam splitter will introduce noise and decoherence. Here we show that heralding techniques can be used to attenuate Schrödinger cat states and squeezed vacuum states without any noise or decoherence [Mičuda et al., Phys. Rev. Lett. 109, 180503 (2012)].
We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information.
The one-clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single qubit of the initial state is pure and others are maximally mixed. Although the model is not universal, it can efficiently solve several problems whose classical efficient solutions are not known.
In this paper we reveal the rich ground-state properties induced by the strong nonlinear atom-photon interaction, which has been found in the recent experiment about a Bose-Einstein condensate coupling with a high-finesse cavity [Nature (London) 464, 1301 (2010)]. Two detuning-dependent phase diagrams are revealed by ...
Relations among von Neumann entropies of different parts of an $N$-partite quantum system have direct impact on our understanding of diverse situations ranging from spin systems to quantum coding theory and black holes. Best formulated in terms of the set $\Sigma^*_N$ of possible vectors comprising the entropies of th...
A central question in quantum information theory and computational complexity is how powerful nonlocal strategies are in cooperative games with imperfect information, such as multi-prover interactive proof systems. This paper develops a new method for proving limits of nonlocal strategies that make use of prior entang...
It is a general fact that the coupling constant of an interacting many-body Hamiltonian do not correspond to any observable and one has to infer its value by an indirect measurement. For this purpose, quantum systems at criticality can be considered as a resource to improve the ultimate quantum limits to precision of ...
We present the results of a numerical study, with 20 qubits, of the performance of the Quantum Adiabatic Algorithm on randomly generated instances of MAX 2-SAT with a unique assignment that maximizes the number of satisfied clauses. The probability of obtaining this assignment at the end of the quantum evolution measu...
The fast and faithful preparation of the ground state of quantum systems is a challenging task but crucial for several applications in the realm of quantum-based technologies. Decoherence poses a limit to the maximum time-window allowed to an experiment to faithfully achieve such desired states.
We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear inequalities, which the spectrum has to verify.
Device-independent quantum key distribution allows for proving the security of a shared cryptographic key between two distant parties with potentially untrusted devices. The security proof is based on the measurement outcome statistics (correlation) of a Bell experiment, and security is guaranteed by the laws of quant...
The Wannier-Stark localization dynamically alters the entanglement behavior of non-Hermitian free fermions. Utilizing the single-particle correlation matrix technique, we analyze the effective Hamiltonian of these fermions with a Wannier-Stark ladder.
The Navier-Stokes equation contains two terms which have been subjected to slight modification: (a) the viscosity term depends of time (the viscosity in average on time is zero, but its variance is non-zero),
Testing and verifying imperfect multi-qubit quantum devices are important as such noisy quantum devices are widely available today. Bell inequalities are known useful for testing and verifying the quality of the quantum devices from their nonlocal quantum states and local measurements.
In this paper we firstly obtain two kinds of effective spectral density functions by setting the cut-off frequencies of baths be infinite and finite. Secondly, we investigate the reduced dynamics of open qubits in four kinds of systems constructed with the basic spin-boson model.
The interconnection of quantum nodes holds great promise for scaling up quantum computing units and enabling information processing across long-distance quantum registers. Such quantum networks can be realized using superconducting qubits linked by waveguides, which facilitate fast and robust on-demand quantum informa...
The purpose of fingerprinting is to compare long messages with low communication complexity. Compared with its classical version, the quantum fingerprinting can realize exponential reduction in communication complexity.
Quantum state tomography (QST) is the process of reconstructing the complete state of a quantum system (mathematically described as a density matrix) through a series of different measurements. These measurements are performed on a number of identical copies of the quantum system, with outcomes gathered as frequencies...
In the Knill-Laflamme-Milburn (KLM) scheme, the success probability of quantum teleportation is given by ${n \over n+1}$, wehre $2n$ is the number of the ancilla qubits. For the high-fidelity approach in the KLM scheme, the success probability is approximately given by $1-{1 \over n^{2}}$ for large $n$.
We address the issue of how to properly treat, and in a more general setting, the concept of a weak value of a weak measurement in quantum mechanics. We show that for this purpose, one must take in account the effects of the measuring process on the entire phase space of the measuring system.
We propose a theoretical scheme for quantum sensing of temperature close to absolute zero in a quasi-one-dimensional Bose-Einstein condensate (BEC). In our scheme, a single-atom impurity qubit is used as a temper-ature sensor.
The first law of thermodynamics, which governs energy conservation, is traditionally formulated as an equality. Surprisingly, we demonstrate that the first law alone implies a universal Landauer-like inequality linking changes in system entropy and energy.
In the paper, we develop a bosonic quantum error correction code based on squeezed Fock states. We compare our proposed code with one based on squeezed Schrodinger's cat states using the Knill-Laflamme cost function and the Petz map fidelity.
Classical, interferometric, optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon abso...

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