标题： 渐近量子态区分对于单位相关态的混合物 显示英文标题

标题： Asymptotic Quantum State Discrimination for Mixtures of Unitarily Related States

摘要： 给定一个状态的混合，找到一种最优区分其元素的方法是量子通信理论中的一个突出问题。 在本文中，我们将研究通过单参数酉群的元素进行酉等价的密度算子的混合，以及相应的量子态区分（QSD）问题。 我们特别关注当时间趋于无穷时的QSD。 我们首先提出一种在可数混合情况下的QSD方法，并解决相应的渐近QSD优化问题，证明在渐近情况下获得最小误差的必要和充分条件（在这种情况下，我们说QSD是完全可解的）。 然后，我们概述一种处理不可数混合的类似方法，并提出一些猜想，这些猜想反映了针对可数混合情况所呈现结果的对应结果。 作为技术工具，我们证明并使用了众所周知的Barnum-Knill界限的无限维版本。 显示英文摘要

摘要： Given a mixture of states, finding a way to optimally discriminate its elements is a prominent problem in quantum communication theory. In this paper, we will address mixtures of density operators that are unitarily equivalent via elements of a one-parameter unitary group, and the corresponding quantum state discrimination (QSD) problems. We will be particularly interested in QSD as time goes to infinity. We first present an approach to QSD in the case of countable mixtures and address the respective asymptotic QSD optimization problems, proving necessary and sufficient conditions for minimal error to be obtained in the asymptotic regime (we say that in such a case QSD is fully solvable). We then outline an analogous approach to uncountable mixtures, presenting some conjectures that mirror the results presented for the cases of countable mixtures. As a technical tool, we prove and use an infinite dimensional version of the well-known Barnum-Knill bound.