Quantum Information Processing最新文献

An important reason why it is currently difficult to unify relativity theory and quantum theory is the quantum information paradox. The information engulfment pointed out by general relativity violates the principles of quantum mechanics. An important reason why the industry does not have a clear understanding of this phenomenon is the current lack of a theoretically solvable cosmological model. Based on the complete model of loop quantum theory, this article solves different levels of Hamiltonian constraint models and simulates black hole information transfer dynamics, especially at extreme points, from analytical results to step-by-step quantum corrections, and attempts to compare the performance of different physical models in simulating quantum advantages during information transmission. Our study shows that even second-order expansions are sufficient to distinguish differences in dynamics at the black hole extremes, but to truly identify a model that has the potential to describe quantum information transfer mechanisms and is significantly different from other models, the theoretical analytical solution should at least extend to level three and above. In addition, the research results such as computational simulation methods and related conclusions cited and improved in this article can provide certain theoretical support and new insights for the research prospects of general relativity loop quantum cosmology and the intersection of quantum information and quantum fields.

We use an artificial neural network (ANN) model to identify the entanglement class of an experimentally generated three-qubit pure state drawn from one of the six inequivalent classes under stochastic local operations and classical communication (SLOCC). The ANN model is also able to detect the presence of genuinely multipartite entanglement (GME) in the state. We apply data science techniques to reduce the dimensionality of the problem, which corresponds to a reduction in the number of required density matrix elements to be computed. The ANN model is first trained on a simulated dataset containing randomly generated states and is later tested and validated on noisy experimental three-qubit states cast in the canonical form and generated on a nuclear magnetic resonance (NMR) quantum processor. We benchmark the ANN model via support vector machines (SVMs) and K-nearest neighbor (KNN) algorithms and compare the results of our ANN-based entanglement classification with existing three-qubit SLOCC entanglement classification schemes such as 3-tangle and correlation tensors. Our results demonstrate that the ANN model can perform GME detection and SLOCC class identification with high accuracy, using a priori knowledge of only a few density matrix elements as inputs. Since the ANN model works well with a reduced input dataset, it is an attractive method for entanglement classification in real-life situations with limited experimental data sets.

In the present work, the randomness measure based on the disentropy of the autocorrelation function is used to quantify the randomness of binary sequences produced by quantum random number generators (QRNG). A homemade QRNG based on vacuum fluctuations and the Quantis QRNG, developed by IDQuantique and whose data are available at http://qrng.ethz.ch/live/, are analyzed. Our results show that the disentropy of the autocorrelation is a useful tool for performance analysis of QRNGs.

In this article, we first obtain a characterization of relationships between pairwise linearly independent (PLI) rank-1 POVMs and Hamel bases for ({mathbb {C}}^{d}). By utilizing the obtained relationships, a necessary and sufficient condition is provided for the set of incoherent states based on PLI rank-1 POVM to be empty. Secondly, we deduce a detailed characterization of incoherent pure states based on a PLI rank-1 POVM. Finally, by properties of rank-1 POVMs and equioverlapping measurements, we give some relationships between weak values of an observable and its trace and expectations.

Coherence is a fundamental feature of quantum mechanics and plays a crucial role in quantum information. In recent years, the quantification of coherence has aroused great interest, and various coherence quantifiers have appeared. We evaluate average coherence of a quantum state based on the modified generalized Wigner–Yanase–Dyson skew information with respect to all orthonormal bases as well as with respect to arbitrary mutually unbiased bases, and demonstrate their equivalence. We further evaluate average variance and average modified generalized variance, and establish several trade-off relations between them and linear entropy, the Brukner–Zeilinger invariant information and average coherence based on the Hilbert–Schmidt norm. In addition, we introduce two kinds of maximal coherence of a quantum state based on the modified generalized Wigner–Yanase–Dyson skew information and metric-adjusted skew information, respectively. Both of them extend the existing maximal coherence based on the Wigner–Yanase skew information and Wigner–Yanase–Dyson skew information. At the same time, it is verified numerically that the maximal coherence is almost equivalent to the average coherence in high-dimensional systems.

To effectively guarantee the authorized communication between the participants and further enhance the information transmission capacity of the link, a multi-qubit hierarchical quantum state sharing protocol with authentication is proposed. First, a type of four-qubit cluster state is generated as the quantum resource, which can be used for the whole process of subsequent authentication and secret sharing, thus eliminating the need to prepare additional entanglement resources. Then, all the agents simply perform Z-basis measurement operations, and the sender can verify that the agents are legitimate, allowing authentication to be conveniently implemented. Finally, depending on the nature of the selected cluster states, the ability of the agent to recover the secret state is asymmetric, and the target quantum state to be shared can be an arbitrary n-qubit state. Furthermore, we validate the correctness of the sharing process for a particular two-qubit state utilizing the IBM simulator and check the security of the proposed protocol against some quantum attacks.

Let ({mathbb {F}}_q) be a finite field, where q is an odd prime power. Let (R={mathbb {F}}_q+u{mathbb {F}}_q+v{mathbb {F}}_q+uv{mathbb {F}}_q) with (u^2=u,v^2=v,uv=vu). In this paper, we study the algebraic structure of ((theta , Theta ))-cyclic codes of block length (r, s) over ({mathbb {F}}_qR.) Specifically, we analyze the structure of these codes as left (R[x:Theta ])-submodules of ({mathfrak {R}}_{r,s} = frac{{mathbb {F}}_q[x:theta ]}{langle x^r-1rangle } times frac{R[x:Theta ]}{langle x^s-1rangle }). Our investigation involves determining generator polynomials and minimal generating sets for this family of codes. Further, we discuss the algebraic structure of separable codes. A relationship between the generator polynomials of ((theta , Theta ))-cyclic codes over ({mathbb {F}}_qR) and their duals is established. Moreover, we calculate the generator polynomials of the dual of ((theta , Theta ))-cyclic codes. As an application of our study, we provide a construction of quantum error-correcting codes (QECCs) from ((theta , Theta ))-cyclic codes of block length (r, s) over ({mathbb {F}}_qR). We support our theoretical results with illustrative examples.

Hirche and Tomamichel recently introduced quantum f-divergence as an integral of quantum Hockey stick divergence. In this paper, we study the optimization of quantum f-divergence between the unitary orbits. The proof relies on the well-known Lidskii’s inequality. We also generalize the result to the mixed unitary orbits.

Given x, y on an unweighted undirected graph G, the goal of the pathfinding problem is to find an x–y path. In this work, we first construct a graph G based on welded trees and define a pathfinding problem in the adjacency list oracle O. Then we provide an efficient quantum algorithm to find an x–y path in the graph G. Finally, we prove that no classical algorithm can find an x–y path in subexponential time with high probability. The pathfinding problem is one of the fundamental graph-related problems. Our findings suggest that quantum algorithms could potentially offer advantages in more types of graphs to solve the pathfinding problem.

Secret Sharing schemes are very much well-developed in classical cryptography. This paper introduces a novel Secret Sharing scheme that leverages entanglement for secure communication. While our protocol initially focuses on a single reconstructor, it offers the flexibility to dynamically change the reconstructor without compromising the reconstruction security of the shared secret. Traditional Secret Sharing schemes often require secure channels for transmitting secret shares to the reconstructor, which can be costly and complex. In contrast, our proposed protocol eliminates the need for secure channels, significantly reducing implementation overhead. Our proposed scheme introduces a secret reconstruction method for (d ge 2), expanding upon previous works that primarily focused on (d > 2.) Our work provides a unified framework that bridges the gap between the cases (d = 2) and (d > 2.) We carefully analyze the conditions under which each case achieves its highest level of security, utilizing newly developed concepts, termed Perfectly Symmetric, Almost Symmetric, and queryless or Vacuously Symmetric entanglements. By eliminating the need for Quantum Fourier Transform and Inverse Quantum Fourier Transform, which were commonly used in previous schemes, we simplify the proposed protocol and potentially improve its efficiency. We thoroughly analyze the correctness and security of our proposed scheme, ensuring its reliability and resistance to certain quantum attacks. Finally, we propose a detailed comparison with the previous works.