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Quantum correlation is a concept in quantum mechanics that describes the correlation between multiple quantum systems or subsystems. It reflects the interdependence between different parts of a quantum state. As an important physical quantity, entropy plays a significant role in the study of quantum correlation, motivated by this idea, we introduce a correlation measure based on the logical entropy, and prove it satisfies the necessary conditions of the given correlation measure, including nonnegativity, invariance under local unitary transformations, adding the auxiliary subsystem correlation measure remains the same. In the end, we obtained the bound of the given correlation measure. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a Lyapunov trajectory tracking design method that incorporates a Schrödinger equation with a dipole subterm and polarizability. Our findings suggest that the proposed control law can overcome the limitations of certain existing control laws that do not converge. By integrating a quadratic performance index, we introduce an optimal control law, which we subsequently analyze for stability and optimality. We also simulate the spin-1/2 particle system to illustrate our results. These findings are further validated through numerical illustrations involving a 3D, 5D system, and a spin-1/2 particle system. [ABSTRACT FROM AUTHOR]

Optical antenna resonators enable control of light‐matter interactions on the nano‐scale via electron–photon hybrid states in strong coupling. Specifically, mid‐infrared (MIR) nano‐antennas coupled to saturable intersubband transitions in multi‐quantum‐well (MQW) semiconductor heterostructures allow for the coupling strength to be tuned through antenna resonance and field intensity. Here, tip‐enhanced nano‐scale variation of antenna‐MQW coupling across the antenna is demonstrated, with a spatially‐dependent coupling strength gaq$g_{\rm aq}$ varying from 73 (strong coupling) to 24 cm−1$\rm {cm}^{-1}$ (weak coupling). This behavior is modeled based on the spatially dependent local constructive and destructive interference between tip and antenna fields. Using a quantum‐mechanical density‐matrix model of the MQW system with its designed values of transition dipole moment, doping density, and population decay time, the picosecond IR pulse coupling to intersubband transitions and the associated tip induced strong‐field saturation effects are described. These results present a new regime of nonlinear IR light‐matter control based on the dynamic manipulation of quantum hybrid states on the nanoscale and in the infrared, with a perspective regarding extension to molecular vibrations. [ABSTRACT FROM AUTHOR]

ABSTRACT This investigation explores the characteristics of electrostatic surface plasma waves within the framework of a spin‐polarized quantum plasma. Utilizing the spin‐polarized quantum hydrodynamic model and incorporating essential elements like Fermi pressure and Bohm potential, we derive the dispersion relation governing surface plasma waves at a plasma–vacuum interface. Through Fourier decomposition of the hydrodynamic model, we establish the dispersion relation that outlines the behavior of surface plasmons under conditions of small amplitude. Quantum effects, encompassing degenerate pressure, and Bohm potential are considered with specific attention given to the spin polarization effect, treating spin up, and spin down electrons as distinct species. The resulting dispersion relation demonstrates that, regardless of the degree of spin matching, Bohm potential significantly alters the phase speed in the limit of a large wave vector. Increasing spin mismatch in the quantum plasma leads to a decrease in the phase speed of the surface mode for a fixed value of the plasmonic coupling parameter H$$ H $$. Our findings bear relevance to graphene‐based plasmonic systems, aligning with some of the observations reported in Gao et al. (2013) and Guo et al. (2019). [ABSTRACT FROM AUTHOR]

Photon-magnon coupling (PMC) integrates microwave or optical photons with magnons, aiming to exploit their distinct strengths in a unified hybrid quantum system, for potential applications in quantum information science and technology. By utilizing numerical simulations, we design a planar hybrid system comprising a hexagonal-ring resonator (HRR) and yttrium iron garnet (YIG) thin film to explore the interaction between microwave photons and magnons. The anti-crossing effects between the HRR's photon mode and the YIG's magnon modes were observed in |S21|-frequency plots under various externally applied magnetic fields. An equivalent theoretical model, based on coupled oscillators, accurately replicated the observed anti-crossing effect and provided estimates for the PMC strength. Furthermore, we explored the behavior of the photon-magnon interaction by altering the position of the YIG film on the HRR's track width, allowing for a more reliable control of the PMC strength variable within the range of 38.78 to 126.6 MHz (nearly 200%) in the planar-geometry HRR/YIG hybrid system. This study opens avenues for designing novel hybrid systems with effective control over the strength of PMC in a planar geometry. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a Lyapunov trajectory tracking design method that incorporates a Schrödinger equation with a dipole subterm and polarizability. Our findings suggest that the proposed control law can overcome the limitations of certain existing control laws that do not converge. By integrating a quadratic performance index, we introduce an optimal control law, which we subsequently analyze for stability and optimality. We also simulate the spin-1/2 particle system to illustrate our results. These findings are further validated through numerical illustrations involving a 3D, 5D system, and a spin-1/2 particle system.

An analytical development is proposed to determine the solution of the motion equations of a charged particle under the influence of an electric field. In the proposal, the advantages and properties of Laplace's transformation are used to map a system of N second-order non-homogeneous differential equations into a system composed of N linear equations. From the most general solution for the dynamics of the system, some particular cases were studied to recover, in a simple way, the results present in the literature. To motivate the study, Ehrenfest's theorem is used and we discuss how the classical results can be interpreted in their quantum version.

This study presents a new approach to solving the problem of synthesis of civil aircraft control based on methods of providing intelligent support and assessing the level of crew training. This implies the representation of flight maneuvers by canonical multidimensional non-stationary models of motion with discrete time and their matrix coefficients identified by empirical data. When performing a flight maneuver in real time, its type is recognized, and then a pattern is extracted from a specialized database to provide the correct way out of the current flight situation. This pattern is the closest to the performed maneuver in the relevance metrics, which makes it possible to calculate the sequence of control parameter vectors according to the desired change in the sequence of the aircraft states. The most interesting in mathematical terms and promising from the viewpoint of practical application, the likelihood metric for trajectories of eigenvalues has provided worse recognition results than other metrics. The study reveals the causes of such a problem and proposes a method for its elimination—quantum filtering based on the analysis of spectra of matrix transformations of flight parameters, representing the aircraft behavior. Clearing these representations from a random "noise" caused by errors in sampling observation, quantum filtering significantly increases the efficiency of recognition of flight fragments compared to a method relying only on the likelihood metric. Applied quantum representations are purely theoretical constructions and do not require for their implementation special computational tools, providing quantum calculations in the usual sense. [ABSTRACT FROM AUTHOR]

Theoretical approaches to quantum many-body physics require developing compact representations of the complexity of generic quantum states. This paper explores an interpretable data-driven approach utilizing principal component analysis (PCA) and autoencoder neural networks to compress the two-particle vertex, a key element in Feynman diagram approaches. We show that the linear PCA offers more physical insight and better out-of-distribution generalization than the nominally more expressive autoencoders. Even with ∼10–20 principal components, we find excellent reconstruction across the phase diagram suggesting the existence of heretofore unrealized structures in the diagrammatic theory. We show that the principal components needed to describe the ferromagnetic state are not contained in the low rank description of the Fermi liquid (FL) state, unlike those for antiferromagnetic and superconducting states, suggesting that the latter two states emerge from pre-existing fluctuations in the FL while ferromagnetism is driven by a different process.

It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast into the form of a neural network with a statistical summation over network parameters. Our simple idea is to use the universal approximation theorem of neural networks to generate arbitrary paths in the Feynman’s path integral. The map can be applied to interacting quantum systems / field theories, even away from the Gaussian limit. Our findings bring machine learning closer to the quantum world.

This study applies computational and numerical techniques to develop some novel and accurate solutions for Gross–Pitaevskii (GP) equations. A quantum system of identical bosons is described using the Hartree–Fock approximation and pseudopotential interaction model by the Gross–Pitaevskii equation (GPE), named after Eugene P. Gross and Lev Petrovich Pitaevskii. Many solitary wave solutions are constructed in various forms based on the implementation of the Khater II method and the novel Kudryashov method. The gained solutions are numerically represented in various graph styles. The validity of the solutions is investigated by applying the septic-B-spline scheme based on calculating the requested conditions from the obtained computational solutions. To make our study more applicable, we study the stability of our solutions by focusing on the Hamiltonian system’s properties. Mathematica 13.1 checks all inputs and outcomes against the original model for further confidence.

In this article, the numerical level representation of imaginary time Green's functions based on a low rank decomposition of the discrete Lehmann spectral representation (DLR) using an effective spectral density has been presented with illustrative efficiency. The DLR basis consists of a collection of exponentials chosen by interpolation decomposition to ensure stable and efficient recovery of imaginary time Green functions or Matsubara frequency samples (Kaye et al., 2022). This implementation to fit behavior of a low-temperature spinless free fermionics-electron gas quantum system requires much fewer degrees of freedom for the standard discretizations. The basic functions of DLR are explicit; carefully chosen to ensure a stable and accurate approach, simplifying standard operations. Importantly, the function can be explicitly transformed to the Matsubara frequency domain or obtained directly by interpolation on a Matsubara frequency grid. [ABSTRACT FROM AUTHOR]

We consider the question as to whether a quantum system is uniquely determined by all values of all its observables. For this, we consider linearly nuclear GB*-algebras over W*-algebras as models of quantum systems. [ABSTRACT FROM AUTHOR]

We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two orthogonal quantum states of a $n_{A}\times n_{B}$ bipartite quantum system can be discriminated via local measurements with an error probability no larger than $\frac {1}2 \left ({1 - \frac {1}{c \min \{n_{A}, n_{B}\}} }\right)$ , where $1\leq c\leq 2\sqrt {2}$ is a universal constant, and our bound scales provably optimally with the local dimensions $n_{A},n_{B}$. Mathematically, this is achieved by showing that the distinguishability norm $\|\cdot \|_{ \mathrm {LO}}$ associated with local measurements satisfies that $\|\cdot \|_{1}\leq 2\sqrt {2} \min \{n_{A},n_{B}\} \|\cdot \|_{ \mathrm {LO}}$ , where $\|\cdot \|_{1}$ is the trace norm. [ABSTRACT FROM AUTHOR]

Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of novel tasks for improving our understanding of the structure of finite-dimensional quantum systems has appeared. In the present article we will concentrate on one aspect of such studies related to the problem of explicit parameterization of state space of an NN-level quantum system. More precisely, we will discuss the problem of a practical description of the unitary SU(N){SU(N)}-invariant counterpart of the NN-level state space BN{\mathcal{B}_N}, i.e., the unitary orbit space BN/SU(N){B_N/SU(N)}. It will be demonstrated that the combination of well-known methods of the polynomial invariant theory and convex geometry provides useful parameterization for the elements of BN/SU(N){B_N/SU(N)}. To illustrate the general situation, a detailed description ofBN/SU(N){B_N/SU(N)} for low-level systems: qubit (N=2{N= 2}), qutrit (N=3{N=3}), quatrit (N=4{N= 4}) - will be given.

We consider the question as to whether a quantum system is uniquely determined by all values of all its observables. For this, we consider linearly nuclear GB*-algebras over W*-algebras as models of quantum systems.

For stochastic quantum systems with measurement feedback, this article proposes a rapid switching control scheme based on state space partition and realizes the rapid stabilization of an eigenstate of an observable operator. Meanwhile, we apply the proposed scheme to the preparation of typical entangled states in multiqubit systems. In view of the convergence obstacle caused by the symmetric structure of the state space, especially in the case with degenerate observable operators, we first partition the state space into a subset containing the target state and its complement to distinguish the target state from its antipodal points, and then design the corresponding control laws in these two subsets, respectively, by using different Lyapunov functions. The interaction Hamiltonians are also constructed to drive the system state to the desired subset first, and further to the target state. In particular, the control law designed in the undesired subset guarantees the strictly monotonic descent of the corresponding Lyapunov function, which makes the system trajectory switch between the two subsets at most twice and has the potential to speed up the convergence process. We also prove the stability of the closed-loop system with the proposed switching control law based on the stochastic Lyapunov stability theory. By applying the proposed switching control scheme to a three-qubit system, we achieve the preparation of a GHZ state and a $W$ state. [ABSTRACT FROM AUTHOR]

A quantum Internet for communicating information encoded in quantum systems over large distances would enable a host of new technologies to be deployed. While exciting progress has been made in small-scale quantum networks, a global quantum Internet will require - like the classical Internet - communicating in a multiple quantum Internet service provider (multi-qISP) setting, with protocols that are oblivious to the global network topology. Here we give a brief overview of quantum networks aimed at those new to the field, present two network-oblivious transport layer protocols for enabling high fidelity communication and performing fault diagnostics, and highlight a number of research opportunities in this nascent field of research. [ABSTRACT FROM AUTHOR]

We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. The resulting optimality conditions depend on the channel considered and on an auxiliary state defined on the output space of the channel. For certain $N$ -qubit classical-quantum channels, we show that codes based on a generalization of Bell states are quasi-perfect and, therefore, they feature the smallest error probability among all codes of the same blocklength and cardinality. [ABSTRACT FROM AUTHOR]

This paper presents a cavity-assisted coherent feedback scheme to cool a mechanical resonator to the ground-state in a weak optomechanical coupling setup. Based on the theory of sideband cooling, resolved sideband regime is a mandatory condition for the ground-state cooling (GSC) in optomechanical systems. Assisted cooling and feedback cooling methods have been proposed and shown to be beneficial for cooling in unresolved sideband cases. In this paper, a cooling method is proposed by combining both approaches. In the proposed method, a coherent feedback loop is added to a cavity-assisted optomechanical system to enhance the cooling performance. The proposed feedback aims to reach the mechanical ground-state in the unresolved sideband regime (USR). Rate equations of the mechanical resonator are derived, and then, by applying Fermi’s golden rule and analyzing the fluctuation spectrum of the optical force, optimal conditions for cooling are obtained. Results show that applying coherent feedback, improves the cooling performance of the system significantly and it is possible to achieve GSC in USR. Moreover, it is shown that the proposed method is capable of cooling the mechanical resonator to much lower energy levels than it is achievable in cavity assisted method. [ABSTRACT FROM AUTHOR]

We introduce and analyse the problem of encoding classical information into different resources of a quantum state. More precisely, we consider a general class of communication scenarios characterised by encoding operations that commute with a unique resource destroying map and leave free states invariant. Our motivating example is given by encoding information into coherences of a quantum system with respect to a fixed basis (with unitaries diagonal in that basis as encodings and the decoherence channel as a resource destroying map), but the generality of the framework allows us to explore applications ranging from super-dense coding to thermodynamics. For any state, we find that the number of messages that can be encoded into it using such operations in a one-shot scenario is upper bounded in terms of the information spectrum relative entropy between the given state and its version with erased resources. Furthermore, if the resource destroying map is the twirling channel over some unitary group, we find matching one-shot lower bounds as well. In the asymptotic setting where we encode into many copies of the resource state, our bounds yield an operational interpretation of resource monotones such as the relative entropy of coherence and its corresponding relative entropy variance. [ABSTRACT FROM AUTHOR]

An approach to simplification of solving diagnostics problems by convolution of applied Markovian models into the quantum representations is presented. These representations imply entanglement by measuring, quantitative estimating the fit between a closed qubit system and observations to identify qubit parameters, and the specialized spectral metric for comparing trajectories of passing state clusters. The obtained advantages are: no needs to take into account transitions between the model states and the elements of transition probability matrices during all the diagnostic procedure, number of qubits determined by the calculated state clusters is several times less than the number of states in an original Markovian process, observed are only stays in the state clusters under consideration. Therefore only the significant information is analyzed to form diagnostic decisions, with quantum spectral analysis revealing intrinsic rules of qubit behaviors. [ABSTRACT FROM AUTHOR]

We consider the most general finite-dimensional quantum mechanical information source, which is given by a quantum system $A$ that is correlated with a reference system $R$. The task is to compress $A$ in such a way as to reproduce the joint source state $\rho ^{AR}$ at the decoder with asymptotically high fidelity. This includes Schumacher’s original quantum source coding problem of a pure state ensemble and that of a single pure entangled state, as well as general mixed state ensembles. Here, we determine the optimal compression rate (in qubits per source system) in terms of the Koashi-Imoto decomposition of the source into a classical, a quantum, and a redundant part. The same decomposition yields the optimal rate in the presence of unlimited entanglement between compressor and decoder, and indeed the full region of feasible qubit-ebit rate pairs. [ABSTRACT FROM AUTHOR]

In (Qi et al. in J Phys A Math Theor 50(28):285301, 2017), the authors proposed a coherence measure based on concurrence measure and obtained a relation between the coherence measure and concurrence entanglement measure. In this paper, motivated by this idea, we introduce an entanglement measure based on the Hellinger distance for bipartite quantum states and prove that it satisfies the necessary conditions of entanglement measure. Furthermore, we obtained a relation between the given entanglement measure and quantum coherence measure based on Hellinger distance. [ABSTRACT FROM AUTHOR]

Physical platforms such as trapped ions suffer from coherent noise that does not follow a simple stochastic model. Stochastic errors in quantum systems occur randomly but coherent errors are more damaging since they can accumulate in a particular direction. We consider coherent noise acting transversally, giving rise to an effective error which is a $Z$ -rotation on each qubit by some angle $\theta $. Rather than address coherent noise through active error correction, we investigate passive mitigation through decoherence free subspaces. In the language of stabilizer codes, we require the noise to preserve the code space, and to act trivially (as the logical identity operator) on the protected information. Thus, we develop necessary and sufficient conditions for all transversal $Z$ -rotations to preserve the code space of a stabilizer code. These conditions require the weight- $2~Z$ -stabilizers to cover all the qubits that are in the support of the $X$ -component of some stabilizer. Furthermore, the weight- $2~Z$ -stabilizers generate a direct product of single-parity-check codes with even block length. By adjusting the sizes of these components, we are able to construct a large family of QECC codes oblivious to coherent noise, one that includes the $[[4L^{2}, 1, 2L]]$ Shor codes. The Shor codes are examples of constant excitation codes, where logical qubits are encoded as a code state that is a sum of physical states indexed by binary vectors with the same weight. Constant excitation codes are oblivious to coherent noise since a transversal $Z$ -rotation acts as a global phase. We prove that a CSS code is oblivious to coherent noise if and only if it is a constant excitation code, and that if the code is error-detecting, then the (constant) weights in different cosets of the $X$ -stabilizers are identical. [ABSTRACT FROM AUTHOR]

In quantum private information retrieval (QPIR), a user retrieves a classical file from multiple servers by downloading quantum systems without revealing the identity of the file. The QPIR capacity is the maximal achievable ratio of the retrieved file size to the total download size. In this paper, the capacity of QPIR from MDS-coded and colluding servers is studied for the first time. Two general classes of QPIR, called stabilizer QPIR and dimension-squared QPIR induced from classical strongly linear PIR are defined, and the related QPIR capacities are derived. For the non-colluding case, the general QPIR capacity is derived when the number of files goes to infinity. A general statement on the converse bound for QPIR with coded and colluding servers is derived showing that the capacities of stabilizer QPIR and dimension-squared QPIR induced from any class of PIR are upper bounded by twice the classical capacity of the respective PIR class. The proposed capacity-achieving scheme combines the star-product scheme by Freij-Hollanti et al. and the stabilizer QPIR scheme by Song et al. by employing (weakly) self-dual Reed–Solomon codes. [ABSTRACT FROM AUTHOR]

A new kind of quantum random walks, called partially open quantum random walks (POQRW, for short), has been studied and developed by Sheng Xiong et al. in (J Stat Phys 152:473–492, 2013). In this paper, some properties of POQRW on the Z d are obtained, to some extent, which extend the results of Ref (Sinayskiy in Phys Scr T151:4077, 2014). We obtain a central limit theorem and a large deviation principle for the position process (X p) p ∈ N associated with the inhomogeneous POQRWs M p m (n) on the Z d , with internal space ħ = C 2 . [ABSTRACT FROM AUTHOR]

The effect of bonding position on the energy conversion efficiency of porphin graphene nanoribbons coupled thermoelectric devices was studied by the first-principles. The results show that the change of bonding position can greatly adjust the lattice thermal conductivity of the coupled thermoelectric devices; although the change of bonding position has no obvious effect on the transport properties of holes in the coupled structure, it can obviously adjust the transport properties of electrons, resulting in the different Seebeck coefficients and quality merit values of different coupled thermoelectric devices The results illustrate the different thermoelectric energy conversion effects in different porphin graphene nanoribbons coupled thermoelectric devices with different bonding positions, which provides an effective theoretical basis for the design of thermoelectric quantum devices based on graphene nanoribbons. [ABSTRACT FROM AUTHOR]

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This article presents a compact quantum threshold voltage (${V}_{\text {th}}$) shift model for a junctionless (JL) quadruple-gate (QG) FET in subthreshold region. Starting from our previous compact model for JL QG FET, the potential and the classical electron density are calculated. Considering 2-D quantum confinement, four types of quantum systems are modeled as a combination of quantum harmonic oscillator (QHO) and quantum well with bottom perturbation potential, depending on the device dimensions. Electron subband energy level for each quantum system is analytically derived to get quantum electron density. The quantum ${V}_{\text {th}}$ shift model is obtained by the ratio of quantum and classical electron line density. The modeling results are validated by 3-D numerical device simulation. It is shown that the proposed model can accurately capture the quantum ${V}_{\text {th}}$ shift in JL QG FET where both fin width and height are 3 nm. Therefore, the proposed ${V}_{\text {th}}$ shift model can be used for quantum corrections for circuit simulation of JL QG FETs. [ABSTRACT FROM AUTHOR]

The formal quantum systems under study demonstrate significant capabilities for solving classification problems in studying dynamical behavior of stochastic systems. Among their features are entanglement by measuring, quantitative estimating the fit for a closed qubit system and observations to identify qubit representation parameters, the specialized discretized spectral metric for comparing patterns of system behaviors, with the multidimensional scaling, cluster analysis and discriminant analysis being applied to the matrices of mutual distances calculated using the presented discretized spectral metric. Hidden evolution periodicities during the observation time period are determined by means of the quantum systems spectral analysis to clarify the system behavior structure. These systems can be also used for representing the Markovian processes with the aid of qubit representations of staying in the corresponding states. An illustrative example revealed diagnostic benefits of the new technique as compared with one based on the Markovian representation. [ABSTRACT FROM AUTHOR]

High fidelity operation of a quantum system requires precise tuning of control parameters. Calibration of a quantum system is often achieved by running complex series of dependent experiments and a full system calibration can require tens of calibration experiments to complete. Optimal control parameters drift over time, and components of experimental quantum systems are susceptible to failure. Hence, continuous operation of a quantum system requires automated background processes such as frequent recalibration and monitoring. In this article, we present a scheduling toolkit that schedules experiments based on a directed acyclic graph using a configurable traversal algorithm. Our scheduler can be triggered from any process, enabling universal feedback between the scheduler and the quantum control system. To demonstrate the capabilities of our system, we implemented a complex system calibration algorithm based on our scheduling toolkit. [ABSTRACT FROM AUTHOR]

Quantum private information retrieval (QPIR) is a protocol in which a user retrieves one of multiple files from n non-communicating servers by downloading quantum systems without revealing which file is retrieved. As variants of QPIR with stronger security requirements, symmetric QPIR is a protocol in which no other files than the target file are leaked to the user, and t-private QPIR is a protocol in which the identity of the target file is kept secret even if at most t servers may collude to reveal the identity. The QPIR capacity is the maximum ratio of the file size to the size of downloaded quantum systems, and we prove that the symmetric t-private QPIR capacity is min{1, 2(n−t)/n} for any 1 ≤ t < n. We construct a capacity-achieving QPIR protocol by the stabilizer formalism and prove the optimality of our protocol. The proposed capacity is greater than the classical counterpart. [ABSTRACT FROM AUTHOR]

We consider the problem of testing two hypotheses of quantum operations in a setting of many uses where an arbitrary prior probability distribution is given. The Chernoff exponent for quantum operations is investigated to track the minimal average error probability of discriminating two quantum operations asymptotically. We answer the question, “When is the Chernoff exponent for quantum operations finite?” We show that either two quantum operations can be perfectly distinguished with finite uses, or the minimal discrimination error decays exponentially with respect to the number of uses asymptotically. That is, the Chernoff exponent is finite if and only if the quantum operations can not be perfectly distinguished with finite uses. This rules out the possibility of super-exponential decay of error probability. Upper bounds of the Chernoff exponent for quantum operations are provided. [ABSTRACT FROM AUTHOR]

Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, a novel quantum detector tomography method is proposed. First, a series of different probe states are used to generate measurement data. Then, using constrained linear regression estimation, a stage-1 estimation of the detector is obtained. Finally, the positive semidefinite requirement is added to guarantee a physical stage-2 estimation. This Two-stage Estimation (TSE) method has computational complexity $O(nd^{2}M)$ , where $n$ is the number of $d$ -dimensional detector matrices and $M$ is the number of different probe states. An error upper bound is established, and optimization on the coherent probe states is investigated. We perform simulation and a quantum optical experiment to testify the effectiveness of the TSE method. [ABSTRACT FROM AUTHOR]

We study the transmission and reflection properties of a single-photon pulse in a one-dimensional waveguide side coupled with a Jaynes-Cummings system, namely, a multi-cavity with an embedded Rydberg atom. A Single-photon pulse is applied to tune the atoms energy spectrum, and varying it can bring the atomic qubit transition on or off-resonance for the cavity. The transmission and reflection behavior are systematically explored by a real-space model Hamiltonian and we find that the coupling strength between the waveguide and the side optical cavity exerts a tremendous impact on it. The influence of cavity and atomic dissipations and the incident pulse width on the transport properties of the single-photon is also investigated simultaneously. Based on these phenomena, we point out the possibility of utilizing this system as a single-photon transport in practice and has potential applications in quantum information.

Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semiclassical Schrödinger equation, where the control variable is the potential given by an external field that may contain uncertainties. Inspired by a relevant work Li et al., 2021 [1] , we incorporate the sampling-based learning process into the training of networks, while combining with the fast time-splitting spectral method for the Schrödinger equation in the semi-classical regime. The numerical results have shown the efficiency and accuracy of our proposed deep learning approach. [ABSTRACT FROM AUTHOR]