Quantum Information Processing最新文献

In this paper, we give a polynomial time algorithm to compute (varphi (N)) for an RSA module N using as input the order modulo N of a randomly chosen integer. This provides a new insight in the very important problem of factoring an RSA module with extra information. In fact, the algorithm is extremely simple and consists only on a computation of a greatest common divisor, two multiplications and a division. The algorithm works with a probability of at least (1-frac{1}{N^{1/2-epsilon }}), where (epsilon ) is any small positive constant.

Quantum visual secret sharing is a novel and important research direction. It has higher security and practicality. However, current schemes are designed for the sharing and recovery of a single secret image. To address this problem, we propose a novel (2,2) quantum visual multi-secret sharing (QVMSS) scheme. In the sharing phase, a quantum encoding table is designed. The colors of the two secret images are entangled and encoded into four different quantum superposition states, which are then distributed to the participants. All secret images are recovered using quantum OR operation and quantum shift operation in the recovery phase. We conducted experiments on a set of 20 standard halftone images to test the feasibility of our proposed scheme. Our scheme can completely recover all the secrets while improving the efficiency and security compared to traditional schemes.

The magic state injection process is a critical component of fault-tolerant quantum computing, and numerous studies have been conducted on this topic. Many existing studies have focused on square-lattice structures, where each qubit connects directly to four other qubits via two-qubit gates. However, hardware that does not follow a lattice structure, such as IBM’s heavy-hexagon structure, is also under development. In these non-lattice structures, many quantum error correction (QEC) codes designed for lattice-based system cannot be directly applied. Adapting these codes often requires incorporating additional qubits, such as flag qubits. This alters the properties of the QEC code and introduces new variables into the magic state injection process. In this study, we implemented and compared the magic state injection process on a heavy-hexagon structure with flag qubits and a lattice structure without flag qubits. Additionally, we considered biased errors in superconducting hardware and investigated the impact of flag qubits under these conditions. Our analysis reveals that the inclusion of flag qubits introduces distinct characteristics into the magic state injection process, which are absent in systems without flag qubits. Based on these findings, we identify several critical considerations for performing magic state injection on heavy-hexagon systems incorporating flag qubits. Furthermore, we propose an optimized approach to maximize the efficacy of this process in such systems.

Quantum secret sharing plays an important role in quantum cryptography. When the deception occurs in quantum secret sharing scheme, the dishonest participant may obtain the secret exclusively. To address this, researchers have developed fair quantum secret sharing schemes to ensure the fairness of obtaining the secret among participants. However, we point that existing schemes achieve fairness at the significant cost of both efficiency and practicality. In this work, firstly, we propose a new fairness framework. Using our fairness framework, it is the first time that the scheme achieves fairness independent of the total round number k of reconstruction set in scheme. Compared to existing schemes that require big enough k to ensure fairness, our new method removes the obstacles to reducing rounds of reconstruction and significantly improving the scheme’s efficiency. Furthermore, our fairness framework can be used for all existing fair quantum secret sharing schemes to significantly reduce the rounds of reconstruction and improve the efficiency of the scheme. Secondly, we present an efficient verification mechanism for reconstructed parameters, which reduces computational cost and complexity compared to existing approaches. Lastly, combining fairness framework and efficient verification mechanism, a new and efficient fair quantum secret sharing scheme is proposed. Our scheme achieves fairness in just 2 rounds of reconstruction with less verification cost. Compared with existing fair quantum secret sharing schemes, our scheme has greatly improved the efficiency and enhanced the practicality.

Designing a mixed quantum channel is challenging due to the complexity of the transformations and the probabilistic mixtures of more straightforward channels involved. Fully characterizing a quantum channel generally requires preparing a complete set of input states, such as a basis for the state space, and measuring the corresponding output states. In this work, we begin by investigating a single input–output pair using projected gradient dynamics. This approach applies optimization flows constrained to the Stiefel manifold and the probabilistic simplex to identify the original quantum channel. The convergence of the flow is guaranteed by its relationship to the Zariski topology. We present numerical investigations of models adapted to various scenarios, including those with multiple input–output pairs, highlighting the flexibility and efficiency of our proposed method.

We propose a dynamic multi-party quantum key exchange (QKE) protocol based on GHZ states to address the challenges of dynamic participation and security in quantum networks. The protocol employs an election algorithm to select initial leaders and primarily uses four-particle GHZ states, with adaptive switching to three-particle GHZ or Bell states as needed. This adaptive resource allocation integrates the strengths of quantum key agreement (QKA) and quantum key distribution (QKD), enhancing scalability and qubit efficiency. During QKA, initial leaders apply Pauli operations on GHZ states to generate correlated keys, while QKD flexibly adjusts to participant numbers to minimize resource consumption. Hash-based verification ensures resistance to common attacks, removes the need for pre-shared keys, and enables secure, scalable key exchange in dynamic multi-party settings.

Graph-structured data commonly arise in many real-world applications, and this extends naturally into the quantum setting, where quantum data with inherent graph structures are frequently generated by typical quantum data sources. However, existing state-of-the-art models often lack training and evaluation on deeper quantum neural networks. In this work, we design a hybrid quantum-classical neural network with deep residual learning, termed Res-HQCNN, specifically designed to handle graph-structured quantum data. Building upon this architecture, we systematically explore the interplay between residual block structures and graph information in both training and testing phases. Through extensive experiments, we demonstrate that incorporating graph structure information into the quantum data significantly improves learning efficiency compared to the existing model. Additionally, we conduct comparative experiments to evaluate the effectiveness of residual blocks. Our results show that the residual structure enables deeper Res-HQCNN models to learn graph-structured quantum data more efficiently and accurately.

This manuscript presents a novel quantum image encryption scheme that integrates two independent two-dimensional (2D) Arnold cat maps—one for spatial permutation and one for intensity permutation—with a robust chaotic diffusion process. This unified dual-permutation framework–applying independent permutations to spatial and intensity data–distinguishes itself from prior dual-map approaches and, to our knowledge, has not been previously explored in QIE. The algorithm features dual permutation, where independent cat maps are applied to coordinate and nibble-split pixel data, followed by quantum diffusion implemented through bit-plane cyclic shifts, chaotic key-based modular addition, and intra-qubit XOR operations. Critically, we provide the explicit formulation of the mathematical operators governing these quantum state transformations, addressing a key limitation of prior works. Moreover, since the proposed encryption transformations are formulated in terms of unitary quantum operators, the scheme is scalable, ensuring that our mathematical framework remains valid for future fault-tolerant quantum computers. This approach ensures that both spatial and intensity information are thoroughly scrambled, resulting in cipher images with near-uniform histograms, near-zero correlation coefficients, and extreme key sensitivity. The quantum implementation offers a theoretical exponential speedup in circuit depth compared to classical (O(R cdot N^2)) time complexity counterparts while resisting statistical, differential, and brute-force attacks through chaotic parameterization. Comprehensive experimental validation confirms the cryptographic superiority of our scheme: it achieves information entropy values exceeding 7.999, Number of Pixel Change Rate (NPCR) > 99.6%, and Unified Average Changing Intensity (UACI) (sim )33.46% on standard test images, outperforming recent state-of-the-art algorithms.

The k-partite entanglement, which focus on at most how many particles in the global system are entangled but separable from other particles, is complementary to the k-entanglement that reflects how many split subsystems are entangled under partitions of the systems in characterizing multipartite entanglement. Very recently, the theory of the complete k-entanglement measure has been established in [Phys. Rev. A 110, 012405 (2024)]. Here we investigate whether we can define the complete measure of the k-partite entanglement. Consequently, with the same spirit as that of the complete k-entanglement measure, we present the axiomatic postulates that a complete k-partite entanglement measure should require. Furthermore, we present two classes of k-partite entanglement measures and show that one is complete while the other one is unified but not complete except for the case of (k=2).

The analytical solution of the system of three-level atom in (Lambda ) configuration interaction with two modes in the presence of a degenerate parameter amplifier term is presented. We investigate the effects of a degenerate parameter amplifier on the quantum properties of the atomic system. Specifically, we analyze how the presence of the parametric amplifier influences the atomic Fisher information, which quantifies the amount of information that can be extracted about a parameter from measurements on the quantum state. Additionally, we study the quantum coherence, which measures the superposition of states, and the second-order correlation function, which provides insights into the statistical properties of the emitted photons. In our analysis, we assumed that the atom in the upper state and the field in the squeezed-pair coherent state. Our results reveal that the presence of the degenerate parameter amplifier significantly enhances the quantum coherence of the atomic states. Furthermore, we demonstrate that the atomic Fisher information, a crucial quantity for parameter estimation in quantum metrology, is substantially influenced by the amplifier’s parameters. The second-order correlation function, which characterizes the statistical properties of the emitted photons, exhibits notable modifications due to the atom-amplifier interaction. These findings provide new insights into the control and manipulation of quantum states in three-level atomic systems, with potential applications in quantum information processing and metrology.