We investigate the impact of the correlation between error gates on the fault-tolerant threshold in quantum circuits under three typical noise models. In the fault-tolerant encoding schemes for two fundamental quantum logical operations, we extend the conventional error injection method by simultaneously applying error gates to both control and target qubits after two-qubit gate operations, with a quantitative characterization of the correlation strength between these error gates. The results show that the fault-tolerant error threshold can be noticeably enhanced by the presence of correlations between error gates, resulting in more robust quantum circuit implementations. We further apply fault-tolerant encoding to the single-qubit teleportation circuit and investigate the effect of correlated noise on its error threshold. The results show that the threshold varies non-monotonically with the correlation strength and that the system's fault-tolerance differs significantly across noise models.

The monogamy and polygamy relations characterize the distributions of quantum entanglement in multipartite systems. We investigate the monogamy relations related to the Rényi-α entanglement (RαE) and polygamy relations related to the RαE of assistance (RαEoA). We present new entanglement monogamy relations satisfied by the η-th (η ≥ 2) power of RαE for α ≥ 2, and by the γ-th (γ ≥ 4) power of RαE for $\frac{\sqrt{7}-1}{2}\,\leqslant \,\alpha \lt 2$, respectively. Moreover, we present polygamy relations satisfied by the tth power of RαEoA with $\frac{\sqrt{7}-1}{2}\,\leqslant \,\alpha \lt \frac{\sqrt{13}-1}{2}$ for 0 ≤ t ≤ 1. We also give relationships among the residual entanglements of RαE and RαEoA, and the three tangle based on our general monogamy relations.

In this study, we propose an experimental scheme to generate macroscopic quantum cat states of a mechanical oscillator within a hybrid atom-optomechanical system. The system consists of a mechanical oscillator harmonically coupled to an optical cavity, where the atom-cavity interaction operates in the ultrastrong-coupling regime described by the Rabi–Stark model. The cavity photon and atom state measurements project the mechanical mirror into cat states, with the process enhanced by Fock-state initialization, nonlinear atom-field coupling and modulated mechanical tuning. Wigner-function analysis confirms nonclassicality. The key findings are: (1) higher initial photon number n increases coherent-state amplitudes and separations of the cat states; (2) smaller detuning improves distinguishability; (3) both the nonlinear atom-photon coupling term and stronger optomechanical coupling accelerate the generation of cat states. This approach provides a parameter-tunable framework for quantum coherence control.

Magic states play an important role in fault-tolerant quantum computation, and so the quantification of magic for quantum states is of great significance. In this work, we propose two new magic quantifiers by introducing two versions of quantum (α, β) Jensen–Shannon divergence, based on the quantum (α, β) entropy and the quantum (α, β)-relative entropy, respectively. We derive many desirable properties for our magic quantifiers, and find that they are efficiently computable in low-dimensional Hilbert spaces. We also show that the initial nonstabilizerness of the input state can boost the magic-generating power for our magic quantifiers with appropriate parameter ranges for a certain class of quantum gates. Our magic quantifiers may provide new tools for addressing some specific problems in magic resource theory.

The growing demand to understand non-equilibrium dynamics in open quantum many-body systems—motivated by progress in quantum simulation and error correction—requires theoretical frameworks that avoid the exponential scaling of the full density matrix. In this work, we develop a first-principles approach to the dissipative hydrodynamical equations of a finite-temperature superfluid. We show that dominant external dissipation not only simplifies the description of intrinsic damping (Beliaev and Landau) but also stabilizes a hydrodynamic formulation. Starting from a density-matrix method aligned with the Zaremba–Nikuni–Griffin formalism, a closed set of dissipative quantum Liouville equations (DQLE) can be obtained. We then introduce a systematic hydrodynamic expansion beyond the conventional Wigner transform, yielding a closed set of dissipative hydrodynamic equations (DHE). Through detailed comparison with the full DQLE, we demonstrate that retaining only the zeroth-order term in the expansion of the anomalous density matrix offers the most accurate and stable DHE implementation, in close agreement with the DQLE under strong dissipation and weak interaction. Our results establish a stabilized hydrodynamic theory for dissipative quantum fluids and significantly reduce the computational complexity of modeling open many-body dynamics.

The precision of quantum measurements can be effectively improved by using both photon-added non-Gaussian operations and Kerr nonlinear phase shift. Here, we employ a coherent state mixed with a photon-added squeezed vacuum state as the input to a Mach–Zehnder interferometer with parity detection, thereby achieving a significant enhancement in phase measurement precision. Our research focuses on the phase sensitivity of linear phase shift under both ideal conditions and photon loss, as well as quantum Fisher information (QFI). The results demonstrate that employing the photon addition operations can markedly enhance phase sensitivity and QFI, and under optimal conditions, the measurement precision can approach the Heisenberg limit for the linear phase shift case. In addition, we delve deeper into the scenario of replacing the linear phase shift with a Kerr nonlinear one and systematically analyze the QFI under both ideal and photon loss conditions. By comparison, it is evident that employing both the photon addition operations and the Kerr nonlinear phase shift can further significantly enhance phase measurement precision while effectively improving the system's robustness against photon loss. These findings are instrumental in facilitating the development and practical application of quantum metrology.

For pure states, the quantum Berry curvature has been well studied. However, the quantum curvature for mixed states has received less attention. From the concept of symmetric logarithmic derivative, we introduce a mixed-state quantum curvature and find that it plays a key role in the field of multi-parameter precision estimations. Through spectral decomposition, we derive the mixed-state Berry curvature for both the full-rank and non-full-rank density matrices. As an example, we obtain the exact expression of the Berry curvature for an arbitrary qubit state.

The theory of multipartite entanglement provides a robust framework for understanding complex phenomena in quantum many-body systems, while multipartite entanglement also serves as a key resource in numerous quantum information processing tasks. Using density matrix renormalization group calculations, we study the multipartite entanglement in one-dimensional quantum long-range ferromagnetic and antiferromagnetic Ising chains with algebraically decaying interactions 1/r^α, respectively. To quantitatively probe the system's multipartite entanglement structure, we employ the quantum Fisher information (QFI). Our results reveal two key behaviors: as the system size increases, the QFI rises, while the multipartite entanglement density decreases and converges toward a constant value. The latter trend points to a fundamental constraint on entanglement distribution in the thermodynamic limit. We further discuss the effects of the magnetic field and the exponent α on the QFI. We find that the peak values of the QFI increase with increasing α. Additionally, the discontinuity in the QFI can be regarded as a powerful tool for characterizing quantum phase transitions in the systems.

Synchronization transmission describes the emergence of coherence between two uncoupled oscillators mediated by their mutual coupling to an intermediate one. In classical star networks, such mediated coupling gives rise to remote synchronization—where nonadjacent leaf nodes synchronize through a nonsynchronous hub—and to explosive synchronization, characterized by an abrupt collective transition to coherence. In the quantum regime, analogous effects can arise from the interplay between 1:1 phase locking and 2:1 phase-locking blockade in coupled spin-1 particles. In this work, we investigate a star network composed of spin-1 particles. For identical oscillators, symmetric and asymmetric dissipation leads to distinct transmission behaviors: remote synchronization and quasi-explosive synchronization appear in different coupling regimes, a phenomenon absent in classical counterparts. For nonidentical networks, we find that at large detuning remote synchronization emerges in the weak-coupling regime and evolves into quasi-explosive synchronization as the coupling increases, consistent with classical star-network dynamics. These findings reveal the rich dynamical characteristics of mediated quantum synchronization and point toward new possibilities for exploring synchronization transmission in larger and more complex quantum systems.

We show that the harmonic and Kepler–Coulomb potentials, supplemented by a singular 1/r² term, can coexist exactly in an N-dimensional space with constant curvature. Unlike existing approaches, which treat these interactions separately or rely on analytical or numerical approximations, our construction is based on a conformal metric that preserves supersymmetry through shape invariance. This coexistence is possible only under the requirement that the effective curvature parameter satisfies τ² > 0, which leads to a unique critical dimension, N = 4, where dynamical compatibility is maximized, even for vanishing angular momentum ℓ = 0. This result shows that curvature acts not merely as a kinematical parameter, but as an active geometric mediator, capable of restoring a hidden symmetry that is broken in flat Euclidean space.

Both irreversibility and incompatibility are important features of quantum channels. Irreversibility of quantum channels characterizes the fundamental limitation in reconstructing information from their outputs. This concept has traditionally been studied for individual channels in a global sense. In this work we generalize the conventional definition of reversible channels to relatively reversible channels, where a quantum channel is reversible relative to another one; thus it is in a relative sense. Incompatibility refers to the impossibility of simultaneously implementing certain pairs of quantum channels, and lies at the very heart of quantum theory. By leveraging the concept of complementary channels, we obtain a direct connection between relative reversibility and channel compatibility. We further propose a quantifier of channel irreversibility in terms of incompatibility between the complementary channels and the identity channel. To illustrate and compare the quantifier of irreversibility with some other quantifiers in the literature, we evaluate them for some prototypical channels. Our results provide insights into the interplay between irreversibility and incompatibility, which may have potential applications in quantum error correction and the resource theory of incompatibility.

Quantum digital signature (QDS) ensures the authenticity, integrity, and non-repudiation of message transmission with information-theoretic security. However, most existing QDS protocols require users to maintain aligned reference frames, which is a complex and time-consuming process, especially in large-scale networks. To overcome this limitation, we propose a reference-frame-independent (RFI)-QDS protocol that eliminates the need for reference frame alignment by utilizing an RFI quantum key distribution technique. Our RFI-QDS protocol enhances signature rates and robustness by bypassing the reference calibration step. This advantage becomes particularly significant under conditions of large reference misalignment. Simulation results demonstrate that our protocol achieves significantly higher signature rates compared to traditional QDS schemes, even in the presence of severe reference misalignment.

We investigate the dynamics of a two-level quantum system driven by a laser pulse characterized by Lorentzian frequency and sub-Lorentzian amplitude modulations. Complete analytical solutions, expressed via confluent Heun functions, are derived. Our analysis reveals that explicit exact analytical solutions exist under infinite sets of specific parameter conditions. The effects of modulation parameters and initial conditions on the final transition probabilities are examined analytically and numerically. Furthermore, the method is demonstrated to be directly applicable to two closely related models with Lorentzian pulses.

Methods of quantum information processing often appear in terms of specially selected states. For example, mutually unbiased bases (MUBs) and symmetric informationally complete measurements are widely applied. Finite frames have found use in many areas including quantum information. Due to its specific inner structure, a single equiangular tight frame (ETF) allows one to formulate criteria to detect non-classical correlations. This study aims to approach entanglement detection with the use of mutually unbiased ETFs. Such frames are an interesting generalization of widely recognized MUBs. It still uses rank-one operators, but the number of outcomes can exceed the dimensionality. Several approaches are considered including separability criteria and entanglement witnesses. Separability criteria for multipartite systems are finally obtained.

We propose a scheme to achieve nonreciprocal single-photon transmission in a system consisting of a spinning whispering-gallery-mode resonator and a stationary resonator containing a scatterer, both coupled to a one-dimensional waveguide. By tuning the Sagnac−Fizeau shift induced by the spinning resonator, high-contrast nonreciprocal transmission in both forward and backward directions can be realized. Furthermore, we investigate the influences of system parameters including waveguide-resonator coupling strength, inter-mode coupling strengths within two resonators, and inter-cavity coupling strength on nonreciprocal transmissions. The results indicate that the synergistic regulation of these parameters can adjust the position of the nonreciprocal transmission peak and achieve high-contrast nonreciprocal transmission.

Multi-valued quantum adder circuits, based on multi-valued logic, are significant components in numerous quantum algorithms. Their low-cost implementations can enhance the efficiency of these algorithms. In this paper, innovative universal architectures for d(d>3)-level quantum half-adder, full-adder, parallel adder, and parallel adder/subtractor circuits are designed using d-level 1-qudit (quantum digit) and M–S gates. To demonstrate the effectiveness of these architectures, quaternary adder circuits derived from them are displayed and compared with several existing counterparts. Judging by the results, these circuits exhibit reductions in quantum cost (QC), hardware complexity (HC), number of constant inputs (NCIs), and number of garbage outputs (NGOs).

In this paper, we investigate the convex roof measures of quantum coherence, with a focus on their superadditive properties. We propose sufficient conditions and establish a framework for coherence superadditivity in tripartite and multipartite systems. Through theoretical derivation, the relevant theorems are given. These results not only expand our understanding of the superadditivity of pure and mixed states but also characterize the conditions under which the superadditivity relations reach equality. Finally, the proposed methods and conclusions are verified through representative examples, providing new theoretical insights into the distribution of quantum coherence in multipartite systems.

In this article, we introduce a new theoretical approach to improve the accuracy of two-dimensional (2D) atomic localization within a tripod-type, four-level atomic system by analyzing its transmission spectrum. In this method, the atom interacts with two orthogonal standing-wave fields and a weak probe field. By examining how the weak probe field passes through the system, we can determine the atom position. Our analysis reveals the presence of both double and sharply defined single localized peaks in the transmission spectrum, which correspond to specific positions of the atom. Importantly, we achieve ultra-high-resolution atomic localization with accuracy confined to a region smaller than λ/32 × λ/32. This level of precision is a significant improvement compared to earlier methods, which had lower localization accuracy. The increased precision is due to the complex interaction between the atom and the carefully controlled standing-wave and probe fields, which allows for precise control over the atom’s position. The implications of this work are significant, especially for applications like nano-lithography, where precise atomic placement is essential, and for laser cooling technologies, where better atomic localization could lead to more effective cooling processes and improved manipulation of atomic states.

Shor’s algorithm outperforms its classical counterpart in efficient prime factorization. We explore the coherence and entanglement dynamics of the evolved states within Shor’s algorithm, showing that the coherence in each step relies on the dimension of register or the order, and discuss the relations between geometric coherence and geometric entanglement. We investigate how unitary operators induce variations in coherence and entanglement, and analyze the variations of coherence and entanglement within the entire algorithm, demonstrating that the overall effect of Shor’s algorithm tends to deplete coherence and produce entanglement. Our research not only deepens the understanding of this algorithm but also provides methodological references for studying resource dynamics in other quantum algorithms.

We investigate phase estimation in a lossy interferometer using entangled coherent states, with a particular focus on a scenario where no reference beam is employed. By calculating the quantum Fisher information, we reveal two key results: (1) the metrological equivalence between scenarios with and without a reference beam, established under ideal lossless conditions for the two-phase-shifting configuration, breaks down in the presence of photon loss, and (2) the pronounced inferior performance of ECSs relative to NOON states, observed in the presence of a reference beam, disappears in its absence.

This work theoretically studies the Bose–Hubbard (BH) model in a ring geometry in a rotating frame. We obtain an effective Hamiltonian by using unitary transformation, where the effect of the rotating reference frame is introducing additional phases to the hopping constant. Within the mean-field theory, the phase transition edge depends not only on the particle number and ring radius, but also on rotation velocity. Therefore, we propose a sensing method of the rotation velocity using the phase transition edge of the Bose–Hubbard model. At the exact phase transition edge where this sensing method is most sensitive, the resolution depends on the rotation velocity, the particle number and the ring radius, while it is independent of the parameters in the Bose–Hubbard model such as the hopping constant and the on-site interaction.

To improve the decoding performance of quantum error-correcting codes in asymmetric noise channels, a neural network-based decoding algorithm for bias-tailored quantum codes is proposed. The algorithm consists of a biased noise model, a neural belief propagation decoder, a convolutional optimization layer, and a multi-objective loss function. The biased noise model simulates asymmetric error generation, providing a training dataset for decoding. The neural network, leveraging dynamic weight learning and a multi-objective loss function, mitigates error degeneracy. Additionally, the convolutional optimization layer enhances early-stage convergence efficiency. Numerical results show that for bias-tailored quantum codes, our decoder performs much better than the belief propagation (BP) with ordered statistics decoding (BP + OSD). Our decoder achieves an order of magnitude improvement in the error suppression compared to higher-order BP + OSD. Furthermore, the decoding threshold of our decoder for surface codes reaches a high threshold of 20%.

We present error-rejecting entanglement concentration protocols (ECPs) for partially entangled electron spins in quantum dots (QDs) with unknown and known parameters using quantum electrodynamics of QDs coupled with optical cavities, which can recover the partially entangled state to the maximally entangled state with unit fidelity even in the non-ideal experimental condition. The error-rejecting ECP for a partially entangled state utilizes parity check operations on electron spins within QDs. Furthermore, for a partially entangled state with known parameters, the ECP is devised through a parameter-splitting approach. The success probabilities of these two error-rejecting ECPs can be further improved by using the resource recycling method and iteration method. On account of their unit fidelity and considerable success probability, the error-rejecting ECPs have promising application value in improving the fidelity of quantum communication.

We investigate phase-controlled bound states in a one-dimensional photonic waveguide coupled to an artificial giant atom at two distant sites. Specifically, we identify the bound state out of the continuum (BOC) and the bound state in the continuum (BIC) and derive the exact existence condition for the BOC. Furthermore, we analytically determine the BIC’s frequency and photonic distribution profile. Remarkably, our analysis reveals quantum beats in both atomic and photonic dynamics, arising from coherent oscillations between the BIC and BOC. These results establish a novel approach for manipulating waveguide quantum electrodynamics via engineered bound states, with potential applications in quantum information processing.

We propose an effective surface plasmon resonance system designed to achieve both negative and positive Goos–Hänchen shifts in reflected light. This system comprises a metal film and an underlying medium, where the real part of the permittivity of the underlying medium must be less than unity. Surface plasmon polaritons can be excited at the lower surface of the metal when light is incident from the air onto the upper surface of the metal. The excitation of surface plasmon polaritons leads to the exploration of the Goos–Hänchen shift (G–HS). Control over the negative and positive (G–HS) is investigated via the wavelength of the incident light. The magnitude of the G–HS is strongly dependent on the incident wavelength. A remarkable enhancement of both negative and positive G–HS in the reflected light is achieved at certain wavelengths and incident angles. Our system paves the way for exploring different characteristics of optical switching and micro-sensors with very high precision.

In this paper, the decoherence dynamics and spectral response of an optomechanical system, with linear and quadratic couplings, is addressed. The decoherence considered arises from pure dephasing, described by the Milburn stochastic evolution of the Schrödinger equation. In the first part of this paper, it is shown how the decoherence rate influences the evolution of the number of phonons, and the quadrature of the mechanical resonator. In the second part of the paper, an attempt to look at the spectral response of the mechanical part of the system is given using non-stationary spectroscopy. The response of the resonator in its equilibrium position is emphasized when the single-photon regime is considered. Coherent states in the cavity field and the mechanical resonator are also represented. Results and discussion comparing the inclusions of the linear, quadratic, and linear-quadratic couplings are given, regarding the influence of the dephasing in the decoherence mechanism.

The Mach–Zehnder interferometer is a fundamental tool for measuring phase shifts between two light paths, serving as a crucial prototype for achieving high-precision measurements in various scientific and technological applications. In this study, we analyze different models for estimating the relative phase shift in a general two-arm Mach–Zehnder interferometer. We demonstrated that single-parameter estimation models can be reduced from the two-parameter estimation model by imposing appropriate constraints on the parameter space. To make quantum Fisher information of the single-parameter estimation models meaningful, the corresponding constraints must be guaranteed in the experiment implementation. Furthermore, we apply the quantum Fisher information approach to analyze the Mach–Zehnder interferometer with the an input state composed of a displaced squeezed vacuum state and a coherent state, providing insights into the precision limits of such configurations.

Nonclassical light fields exhibit unique quantum characteristics that not only expand the scope of optical research but also provide a solid foundation for advancements in quantum technologies. In this study, we investigate a system consisting of one-¹³³Cs atom placed in a resonant cavity. Pumped by 459 nm laser light, the system generates cavity modes corresponding to the atomic 7S_1/2 → 6P_3/2 (1470 nm) and 7S_1/2 → 6P_1/2 (1359 nm) transitions, which are associated with the clock states of the cesium active optical clock. By analyzing the statistical and dynamical properties of the fields, we systematically explore the nonclassical behavior of the system under varying coupling strengths and cavity decay rates. We identify parameter regions where both individual fields and their cross-correlation exhibit nonclassicality, with the Cauchy–Schwarz (CS) violation coefficient R reaching a maximum of 13.9. This demonstrates the system’s ability to generate highly nonclassical photon pairs, enriching the repertoire of nonclassical light sources.

In discrete-variable quantum computation, non-Clifford T-gates play a pivotal role in achieving genuine quantum advantage. However, in the literature, T-gates are only defined for prime dimensional systems, and the absence of their high-dimensional counterparts in non-prime dimensional systems raises the issue of how to introduce certain T-gates in such systems. In continuous-variable quantum computation, universality is achieved through a combination of Gaussian gates and some non-Gaussian gates, such as the widely used cubic phase gates. In this work, we establish some connections between discrete-variable (Clifford/non-Clifford) gates and continuous-variable (Gaussian/non-Gaussian) gates via the powerful GKP (Gottesman–Kitaev–Preskill) encoding, which maps qudits to oscillators and serves as a bridge between discrete and continuous realms. By exploiting the analogies between the Clifford hierarchy and the Gaussian hierarchy, we derive (discrete-variable) T-gates in arbitrary (not necessarily prime) dimensional systems from well established (continuous-variable) cubic phase gates. We reveal some basic properties of the unified T-gates, and make a comparative study of various T-gates. As an application, we employ the T-gates to construct equidistributed n-angular frames and certain MUBs (mutually unbiased bases).

In this paper, we study the problem of sampling complexity for channel discrimination with respect to two different strategies: product strategy and adaptive strategy. We first formally introduce the definitions of the sampling complexity of the channels under the framework of hypothesis testing , wherein the goal is to determine the minimum number of samples needed to reach a desired error probability. We then establish the lower and upper bounds on the sampling complexity of the symmetric, asymmetric, and error exponent hypothesis testing settings. We show that, by imposing product strategy on testing, the bounds are always characterized by the generalized channel divergence, while with adaptive strategy, the bounds are characterized by the amortized channel divergence. Finally, we analyze two concrete examples, and obtain that the adaptive strategy can not lead to an advantage to the problem of determining the sampling complexity for classical-quantum channels, which can bring advantages for generalized amplitude damping channels.

In this paper, we propose a perfect entanglement swapping protocol for generating a shared three-qubit W state between two remote parties in a deterministic manner. Our method offers a reliable alternative to existing probabilistic protocols for W state entanglement swapping, which is crucial for various quantum information processing tasks. We present a detailed quantum circuit design, implemented using the Qiskit simulator, that outlines the preparation of W states and the execution of joint measurements required for the entanglement swapping process. Furthermore, we analyze the effects of imperfect operations and noisy communication channels on the fidelity of the resulting shared W state. To address these challenges, we introduce a weak measurement-based purification method that enhances fidelity in the presence of amplitude damping. Through mathematical analysis and Qiskit simulations, we demonstrate the effectiveness of our proposed protocol, offering a practical solution for high-fidelity W state generation in real-world quantum communication scenarios.

In this work, we mainly study Bell nonlocality and quantum steerability of two-coupled double quantum dots (DQDs) system via local filtering operation. We compare and analyze the influence of the Coulomb potential, temperature, tunneling parameter and local filtering operation on quantum steering and Bell nonlocality in the system. The results show that quantum steering and nonlocality first increase and then decrease but never vanish even for the stronger value of the Coulomb potential. Quantum steering and Bell nonlocality would degrade with the increase of temperature. The filtering process does not increase the degree of steerability, but decreases the range of quantum steerability. In addition, it is noteworthy that a peculiar phenomenon exists: the Einstein–Podolsky–Rosen (EPR) steering asymmetry between Alice and Bob first increase, then decrease to zero and finally increases as the tunneling strength increases. However, this phenomenon does not appear with no operation between Alice and Bob.

Complex numbers play a pivotal role in both mathematics and physics, particularly in quantum mechanics, and are extensively utilized to depict the behavior of microscopic particles. Recognizing the significance of complex numbers, a framework of imaginarity resource theory has recently been established. In this work, we propose two types of imaginarity monotones induced by the unified (α, β)-relative entropy and investigate their properties. Moreover, we give explicit examples to illustrate our results.

The Josephson junction is typically tuned by a magnetic field or electrostatic gate to realize a superconducting (SC) transistor, which manipulates the supercurrent in integrated SC circuits. Here, we propose a theoretical scheme for a light-controlled SC transistor, which is composed of two superconductor leads weakly linked by a coherent light-driven quantum dot. We discover a Josephson-like relation for the supercurrent ${I}_{{\rm{s}}}={I}_{c}({\rm{\Phi }})\,\sin {\rm{\Phi }}$, where both the supercurrent phase Φ and magnitude I_c can be completely controlled by the phase, intensity, and detuning of the driving light. Additionally, the supercurrent magnitude displays a Fano profile with the increase of the driving light intensity, which is understood by comparing the level splitting of the quantum dot under light driving with the SC gap. Moreover, when two such SC transistors form a loop, they constitute a light-controlled SC quantum interference device (SQUID). Such a light-controlled SQUID can demonstrate the Josephson diode effect, and the optimized non-reciprocal efficiency achieves up to 54%, surpassing the maximum record reported in recent literature. Thus, our scheme delivers a promising platform for performing diverse and flexible manipulations in SC circuits.

As one of the famous effects in the quantum Rabi model (QRM), Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts, such as quantum collapse and revival effects. In this paper, we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model. It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions, and the Husimi Q function are more dispersed in phase space. Moreover, we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space. Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.

The Husimi function (Q-function) of a quantum state is the distribution function of the density operator in the coherent state representation. It is widely used in theoretical research, such as in quantum optics. The Wehrl entropy is the Shannon entropy of the Husimi function, and is non-zero even for pure states. This entropy has been extensively studied in mathematical physics. Recent research also suggests a significant connection between the Wehrl entropy and many-body quantum entanglement in spin systems. We investigate the statistical interpretation of the Husimi function and the Wehrl entropy, taking the system of N spin-1/2 particles as an example. Due to the completeness of coherent states, the Husimi function and Wehrl entropy can be explained via the positive operator-valued measurement (POVM) theory, although the coherent states are not a set of orthonormal basis. Here, with the help of the Bayes' theorem, we provide an alternative probabilistic interpretation for the Husimi function and the Wehrl entropy. This interpretation is based on direct measurements of the system, and thus does not require the introduction of an ancillary system as in the POVM theory. Moreover, under this interpretation the classical correspondences of the Husimi function and the Wehrl entropy are just phase-space probability distribution function of N classical tops, and its associated entropy, respectively. Therefore, this explanation contributes to a better understanding of the relationship between the Husimi function, Wehrl entropy, and classical-quantum correspondence. The generalization of this statistical interpretation to continuous-variable systems is also discussed.

We analyze the steady-state characteristics of a damped harmonic oscillator (system) in the presence of a non-Markovian bath characterized by Lorentzian spectral density. Although Markovian baths presume memoryless dynamics, the introduction of complex temporal connections by a non-Markovian environment radically modifies the dynamics of the system and its steady-state behaviour. We obtain the steady-state Green’s function and correlation functions of the system using the Schwinger–Keldysh formalism. In both rotating and non-rotating wave approximation, we analyzed various emergent properties like effective temperature and distribution function. We also explore the impact of dissipation and non-Markovian bath on the quantum Zeno and anti-Zeno effects. We show that a transition between Zeno to anti-Zeno effect can be tuned by bath spectral width and the strength of dissipation.

Recently, large-scale trapped ion systems have been realized in experiments for quantum simulation and quantum computation. They are the simplest systems for dynamical stability and parametric resonance. In this model, the Mathieu equation plays the most fundamental role for us to understand the stability and instability of a single ion. In this work, we investigate the dynamics of trapped ions with the Coulomb interaction based on the Hamiltonian equation. We show that the many-body interaction will not influence the phase diagram for instability. Then, the dynamics of this model in the large damping limit will also be analytically calculated using few trapped ions. Furthermore, we find that in the presence of modulation, synchronization dynamics can be observed, showing an exchange of velocities between distant ions on the left side and on the right side of the trap. These dynamics resemble that of the exchange of velocities in Newton’s cradle for the collision of balls at the same time. These dynamics are independent of their initial conditions and the number of ions. As a unique feature of the interacting Mathieu equation, we hope this behavior, which leads to a quasi-periodic solution, can be measured in current experimental systems. Finally, we have also discussed the effect of anharmonic trapping potential, showing the desynchronization during the collision process. It is hoped that the dynamics in this many-body Mathieu equation with damping may find applications in quantum simulations. This model may also find interesting applications in dynamics systems as a pure mathematical problem, which may be beyond the results in the Floquet theorem.

In this paper, we investigate the effect of exceptional points (EPs) on the violation of Leggett–Garg inequality (LGI) and no-signaling-in-time (NSIT) conditions and compare the different effects between the Hamiltonian EP (HEP) and Liouvillian EP (LEP) on those violations. We consider an open system consisting of two coupled qubits and each qubit is contacted with a thermal bath at a different temperature. In the case of omitting quantum jumps, we find that the system exhibits a second-order HEP, which separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI and NSIT conditions can be violated in both regimes and not violated at the HEP. In the case of without omitting quantum jumps, we find that the system exhibits a third-order LEP, which also separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI can only be violated in the underdamped regime with large coupling strength between the qubits. Conversely, the NSIT conditions can be violated in both regimes, as well as at the LEP, except in the overdamped regime with small coupling strength between the qubits. Comparing the violations of the LGI and NSIT conditions with HEP and LEP, we find that the quantum jumps would reduce the generation of coherence, enhance the decoherence, and lead to narrower parameter regimes that the LGI and NSIT conditions can be violated. Furthermore, in both cases, the NSIT conditions can be violated in a wider parameter regime than the LGI.

We present a theoretical scheme to realize two-dimensional (2D) asymmetric diffraction grating in a five-level inverted Y-type asymmetric double semiconductor quantum wells (SQWs) structure with resonant tunneling. The SQW structure interacts with a weak probe laser field, a spatially independent 2D standing-wave (SW) field, and a Laguerre–Gaussian (LG) vortex field, respectively. The results indicate that the diffraction patterns are highly sensitive to amplitude modulation and phase modulation. Because of the existence of vortex light, it is possible to realize asymmetric high-order diffraction in the SQW structure, and then a 2D asymmetric grating is established. By adjusting the detunings of the probe field, vortex field, and SW field, as well as the interaction length, diffraction intensity, and direction of the 2D asymmetric electromagnetically induced grating (EIG) can be controlled effectively. In addition, the number of orbital angular momenta (OAM) and beam waist parameter can be used to modulate the diffraction intensity and energy transfer of the probe light in different regions. High-order diffraction intensity is enhanced and high-efficiency 2D asymmetric diffraction grating with different diffraction patterns is obtained in the scheme. Such 2D asymmetric diffraction grating may be beneficial to the research of optical communication and innovative semiconductor quantum devices.