Quantum Information Processing最新文献

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.

In this paper, we first study the linear complementary pair (abbreviated to LCP) of codes over finite non-chain rings (R_{u,v,q}={mathbb {F}}_q+u{mathbb {F}}_q+ v{mathbb {F}}_q+uv{mathbb {F}}_q) with (u^2=u,v^2=v). Then we provide a method of constructing entanglement-assisted quantum error-correcting (abbreviated to EAQEC) codes from an LCP of codes of length n over (R_{u,v,q}) using CSS. To enrich the variety of available EAQEC codes, some new EAQEC codes are given in the sense that their parameters are different from all the previous constructions.

Eylee Jung et.al[1] had conjectured that (P_{max}=frac{1}{2}) is a necessary and sufficient condition for the perfect two-party teleportation, and consequently, the Groverian measure of entanglement for the entanglement resource must be (frac{1}{sqrt{2}}). It is also known that prototype W state is not useful for standard teleportation. Agrawal and Pati[2] have successfully executed perfect (standard) teleportation with non-prototype W state. Aligned with the protocol mentioned in[2], we have considered here Star type tripartite states and have shown that perfect teleportation is suitable with such states. Moreover, we have taken the linear superposition of non-prototype W state and its spin-flipped version and shown that it belongs to Star class. Also, standard teleportation is possible with these states. It is observed that genuine tripartite entanglement is not necessary requirement for a state to be used as a channel for successful standard teleportation. We have also shown that these Star class states are (P_{max}=frac{1}{4}) states and their Groverian entanglement is (frac{sqrt{3}}{2}), thus concluding that Jung conjecture is not a necessary condition.

The transmission rate of traditional underwater discrete modulation continuous variable quantum key distribution (CV-QKD) scheme is limited by Nyquist criterion. Considering the limitation of Nyquist criterion and the large attenuation coefficient of the seawater channel, it is a challenge to enhance the secret key rate of the traditional underwater discrete modulation CV-QKD without relying on physical hardware. To solve this problem, we propose an underwater discrete modulation CV-QKD with faster-than-Nyquist (FTN) scheme; namely, a FTN signal generator is employed to make the discrete modulated signals obtain FTN rate at the sender’s side. Then an equalizer and a decoder are used to restore the sampled symbols to the original information by taking four typical seawater channels into account. The simulation results show that compared to the traditional Nyquist transmission scheme, the proposed protocol can effectively improve the secret key rate and underwater secure distance no matter what type of water is considered. These results indicate that the proposed scheme can break the constraints of Nyquist criterion, thus achieving a more efficient underwater discrete modulation CV-QKD scheme. Furthermore, we also consider the finite-size effect, which provides more practical results than those achieved in the asymptotic limit.

Quantum dialogue (QD) is a two-way quantum secure direct communication. Traditional QD protocols rely on transmitting photons through a quantum channel, which can introduce vulnerabilities. This paper presents a counterfactual controlled QD protocol based on entanglement swapping. By employing counterfactual quantum entanglement generation, the protocol facilitates controlled QD without requiring physical particle transfer or prior entanglement between remote participants. This approach significantly enhances the security of QD methods, providing robust resistance against all possible channel-based attacks and ensuring theoretical security.

Secret sharing has become a important cryptographic primitive and been widely used. And quantum secret sharing is a quantum approach to achieve secret sharing. The (t, n) threshold quantum secret sharing requires only t participants out of n to cooperate to recover the secret, which is more flexible than the (n, n) scheme. However, most (t, n) threshold schemes basically involve quantum entanglement, and the preparation of entangled states as well as entanglement swapping are relatively complex. In this paper, we propose a (t, n) threshold quantum secret sharing scheme with authentication by using the Lagrange interpolation polynomial based on single photons. Unlike other (t, n) threshold schemes, it does not involve entangled states or entanglement swapping. And the distributor authenticate the participants without revealing the full identity key. In addition, secret sharing is based on Lagrange interpolation polynomial implementation, allowing any t participants to recover the secret. Analysis shows that the scheme can resist external eavesdroppers and dishonest participants. Compared with other schemes, this scheme has the following advantages: (1) it is easy to implement; (2) the (t, n) threshold scheme increases the flexibility of the scheme; (3) the identity key can be reused.

The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to hardware constraints. In this work, we develop an algorithm that decomposes the QAOA input problem graph into a smaller problem and solves MaxCut using QAOA on the reduced graph. The algorithm requires a subroutine that can be classical or quantum—in this work, we implement the algorithm twice on each graph. One implementation uses the classical solver Gurobi in the subroutine and the other uses QAOA. We solve these reduced problems with QAOA. On average, the reduced problems require only approximately 1/10 of the number of vertices than the original MaxCut instances. Furthermore, the average approximation ratio of the original MaxCut problems is 0.75, while the approximation ratios of the decomposed graphs are on average of 0.96 for both Gurobi and QAOA. With this decomposition, we are able to measure optimal solutions for ten 100-vertex graphs by running single-layer QAOA circuits on the Quantinuum trapped-ion quantum computer H1-1, sampling each circuit only 500 times. This approach is best suited for sparse, particularly k-regular graphs, as k-regular graphs on n vertices can be decomposed into a graph with at most (frac{nk}{k+1}) vertices in polynomial time. Further reductions can be obtained with a potential trade-off in computational time. While this paper applies the decomposition method to the MaxCut problem, it can be applied to more general classes of combinatorial optimization problems.