\(N\)顺序接收器在\(r\geq2\)任意量子态之间的结论性判别

IF 1.7 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
E. R. Loubenets, M. Namkung
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引用次数: 0

摘要

在本文中,我们开发了一个通用的数学框架,用于\(N\geq1\)顺序接收器在每个接收器获得结论性结果的情况下区分\(r\geq2\)量子态。这种类型的鉴别构成了一个接收者最小误差鉴别的\(N\) -顺序扩展。基于量子态仪器的概念,所开发的一般框架,对于任意维度的任意数量\(r\geq2\)纯或混合量子态和任意数量\(N\geq1\)顺序接收器之间的结论性区分是有效的,这使我们能够推导出新的重要的一般结果。特别地,我们找到了一个关于\(r\geq2\)量子态的一般条件,在允许所有类型的接收者量子测量的策略中,这些\(r\geq2\)态之间的\(N\) -顺序决定性鉴别的最优成功概率等于任何数量\(N\geq2\)的后续顺序接收者的第一个接收者的最优成功概率,并指定了相应的最优协议。此外,我们扩展了我们的一般框架,以包括在噪声通信下\(r\geq2\)任意量子态之间的\(N\) -顺序结论性判别。作为一个例子,我们通过去极化量子通道对两个量子比特状态之间的两序列结论性判别进行了解析和数值分析。从理论角度和通过噪声量子信道成功地发展多方量子通信的角度来看,所得到的新的一般性结果都是重要的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Conclusive Discrimination by \(N\) Sequential Receivers between \(r\geq2\) Arbitrary Quantum States

In the present paper, we develop a general mathematical framework for discrimination between \(r\geq2\) quantum states by \(N\geq1\) sequential receivers for the case in which every receiver obtains a conclusive result. This type of discrimination constitutes an \(N\)-sequential extension of the minimum-error discrimination by one receiver. The developed general framework, which is valid for a conclusive discrimination between any number \(r\geq2\) of quantum states, pure or mixed, of an arbitrary dimension and any number \(N\geq1\) of sequential receivers, is based on the notion of a quantum state instrument, and this allows us to derive new important general results. In particular, we find a general condition on \(r\geq2\) quantum states under which, within the strategy in which all types of receivers’ quantum measurements are allowed, the optimal success probability of the \(N\)-sequential conclusive discrimination between these \(r\geq2\) states is equal to that of the first receiver for any number \(N\geq2\) of further sequential receivers and specify the corresponding optimal protocol. Furthermore, we extend our general framework to include an \(N\)-sequential conclusive discrimination between \(r\geq2\) arbitrary quantum states under a noisy communication. As an example, we analyze analytically and numerically a two-sequential conclusive discrimination between two qubit states via depolarizing quantum channels. The derived new general results are important both from the theoretical point of view and for the development of a successful multipartite quantum communication via noisy quantum channels.

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来源期刊
Russian Journal of Mathematical Physics
Russian Journal of Mathematical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
14.30%
发文量
30
审稿时长
>12 weeks
期刊介绍: Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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