Quantum Information Processing最新文献

Based on the Li–Du–Massar quantization scheme, this paper constructs a quantum mixed duopoly game model with quadratic costs, involving one state-owned enterprise aiming to optimize domestic social surplus and one private enterprise focused on maximizing its own profit. Considering the bounded rational expectations of the state-owned enterprise and the naïve expectations of the private enterprise, the nonlinear dynamic behavior of the system is investigated. The existence and stability of the quantum Nash equilibrium are analyzed. Complex dynamical behaviors are comprehensively examined using bifurcation diagrams, the maximum Lyapunov exponents, strange attractors, and sensitive dependence on initial conditions, confirming the emergence of chaos via period-doubling bifurcations. Furthermore, an effective method is proposed to control and restore the system from chaos back to a stable state.

In this paper, we explore the effects of correlated amplitude damping noise and depolarizing noise for quantum steering. We find that adjusting the channel’s correlated parameters can enhance the resilience of quantum steering against decoherence, thereby maintaining the non-local characteristics of quantum systems under noisy conditions. This investigation provides valuable insights for the advancement of quantum communication and information processing technologies, presenting new strategies and theoretical underpinnings for the development of noise-resilient quantum information protocols.

We introduce Merlin–Arthur (MA) automata where Merlin provides a certificate at the beginning of computation and it is scanned by Arthur before reading the input. We define Merlin–Arthur deterministic, probabilistic, and quantum finite state automata (resp., MA-DFAs, MA-PFAs, and MA-QFAs) and postselecting MA-PFAs and MA-QFAs (resp., MA-PostPFA and MA-PostQFA). We present several results using different certificate lengths. We show that MA-DFAs can benefit from only constant-length certificates, and they are equivalent to multi-entry DFAs. Thus, they recognize all and only regular languages, but they can be exponential and polynomial state-efficient over binary and unary languages, respectively. With sublinear-length certificates, MA-PFAs can recognize several nonstochastic unary languages with cutpoint 1/2. With linear-length certificates, MA-PostPFAs can recognize these nonstochastic unary languages with bounded error. With arbitrarily long certificates, bounded-error MA-PostPFAs can verify every unary decidable language. With sublinear-length certificates, bounded-error MA-PostQFAs can verify several nonstochastic unary languages. With linear-length certificates, they can verify every unary language and some NP-complete binary languages. With exponential-length certificates, they can verify every binary language.

This paper proposes a single-qudit quantum neural network for multiclass classification by using the enhanced representational capacity of high-dimensional qudit states. Our design employs a d-dimensional unitary operator, where d corresponds to the number of classes, constructed using the Cayley transform of a skew-symmetric matrix, to encode and process class information compactly. This architecture enables a direct mapping between class labels and quantum measurement outcomes, reducing circuit depth and computational overhead. To optimize network parameters, we introduce a hybrid training approach that combines an extended activation function, derived from a truncated multivariable Taylor series expansion, with support vector machine optimization for weight determination. We evaluate our model on the MNIST and EMNIST datasets, demonstrating competitive accuracy while maintaining a compact single-qudit quantum circuit. Our findings highlight the potential of qudit-based QNNs as scalable alternatives to classical deep learning models, particularly for multiclass classification. However, practical implementation remains constrained by current quantum hardware limitations. This research advances quantum machine learning by demonstrating the feasibility of higher-dimensional quantum systems for resource-efficient learning tasks.

Entanglement distillation is a key task in quantum-information processing. In this paper, we distill non-positive-partial-transpose (NPT) bipartite states of some given Schmidt rank and matrix rank. We show that all bipartite states of Schmidt rank two are locally equivalent to classical-classical states, and all bipartite states of Schmidt rank three are 1-undistillable. Subsequently, we show that low-rank B-irreducible NPT states are distillable for large-rank reduced density operators by proving low-rank B-irreducible NPT state whose range contains a product vector is distillable. Eventually, we present an equivalent condition to distill (Mtimes N) bipartite states of rank (max {M,N}+1).

Characterizing quantum entanglement in mixed states is a longstanding challenge. Among the various methods available, conditional entropies serve as a powerful tool. Notably, the AR q-conditional entropy introduced by Abe and Rajagopal in 2002 has demonstrated significant promise as it often surpasses other entropy-based criteria. The wide-ranging applications of conditional entropy in quantum information underscore the importance of studying and analyzing it for a deeper understanding of quantum correlations and their implications. In this paper, we investigate the non-separability of noisy Dicke states using the AR approach of conditional entropy. Our findings reveal that the entropic criterion is equally effective as the PPT criterion in identifying non-separability across a large subset of N-partite noisy Dicke states with even N and excitation number (k = N/2). Additionally, for systems with (N > 30) and (k=1), the separability thresholds derived from both criteria converge within (10^{-8}), highlighting their strong agreement in this parameter range. Furthermore, we established a condition based on AR q-conditional entropy for identifying genuine multipartite entanglement (GME) in noisy Dicke states and compared its effectiveness to previous methods. Notably, our condition identifies a broader range of GME, particularly when the number of excitations approaches half the number of qubits (i.e., N/2). In contrast, previous methods perform better when the number of excitations is significantly less than N/2. We believe these results will pave the way for further advancements in entanglement theory and the development of potential quantum-based applications for conditional entropy.

This work introduces a dynamic hierarchical quantum secret sharing scheme that utilizes the quantum Fourier transform and the generalized Hadamard gate. In this scheme, the distributor transmits both the secrets, quantum and classical information simultaneously to the participants. The authenticity of the participants is ensured by employing the generalized Bell state. The access structure is flexible and can be modified, allowing the number of participants to increase or decrease, whenever the shared classical secret is updated, without requiring any changes to each of the individual hierarchical secrets held by participants. We examine two scenarios concerning the addition of participants: the first involves incorporating a new participant into an existing level, while the second involves introducing an entirely new level within the hierarchical structure. Additionally, the security analysis demonstrates that the proposed protocol is resilient to intercept-and-resend, collusion, entangle-and-measure, forgery, and denial attacks.

We investigate the dynamics of quantum-state texture (QST) for two uniformly accelerated atoms interacting with a quantized massive scalar field. Our analysis reveals that the system’s evolution arises from a complex competition between local decoherence caused by vacuum fluctuations and a collective, environment-mediated evolution that drives the system to a steady state. This interplay is identified as the physical origin of the notable dip-and-recover phenomenon observed in the QST for certain initial states. The results demonstrate that in the long time limit, the atoms evolve toward a thermal state at the Unruh temperature. We further show how physical parameters regulate this competition: Increasing interatomic separation and field mass can partially protect QST by weakening the collective recovery effect or universally slowing all dissipative processes, respectively. Conversely, higher acceleration enhances the collective thermalization, leading to a faster evolution toward a steady QST value. These insights are significant for understanding and controlling quantum resources in relativistic open quantum systems.

We propose a scheme that induces quantum correlations in optomechanical systems. Our benchmark system consists of two optically coupled optical cavities which interact with a common mechanical resonator. The optical cavities host saturable nonlinearity which triggers either gain or losses in each cavity. Without these nonlinearities, there are no quantum correlations, i.e., entanglement and steering, generated in the system. By turning on the nonlinearities, gain and losses are switched on, enabling flexible generation of both quantum entanglement and quantum steering in our proposal. These generated quantum correlations seem to be insensitive to the induced gain, while the induced losses through saturation effect efficiently enhance quantum correlations. Moreover, the robustness of the generated quantum correlations against thermal fluctuations is further improved under nonlinear saturation scenario. This work suggests a way of using nonlinear saturation effects to engineer quantum correlations even at room temperature, which are useful for quantum information processing, quantum computational tasks, and quantum technologies.

Uncertainty relations are pivotal in delineating the limits of simultaneous measurements for observables. In this paper, we derive four novel uncertainty and reverse uncertainty relations for the sum of variances of two incompatible observables, leveraging the mathematical framework of the Maligranda inequality. These relations are shown to provide highly precise bounds, in some cases outperforming well-known existing relations. Furthermore, we extend these results to multi-observable scenarios by employing an inequality from M. Kato et al., deriving generalized uncertainty relations that similarly exhibit enhanced precision. The incorporation of the phase angle of the measurement state contributes to strengthening the derived inequalities. Comparative analyses with prior studies confirm the effectiveness of our inequalities in two-observable systems via three illustrative examples.