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Symmetric distinguishability as a quantum resource
arXiv - CS - Information Theory Pub Date : 2021-02-24 , DOI: arxiv-2102.12512
Robert Salzmann, Nilanjana Datta, Gilad Gour, Xin Wang, Mark M. Wilde

We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources, i.e., sources that emit one of two possible quantum states with given prior probabilities. Such a source can be represented by a classical-quantum state of a composite system $XA$, corresponding to an ensemble of two quantum states, with $X$ being classical and $A$ being quantum. We study the resource theory for two different classes of free operations: $(i)$ ${\rm{CPTP}}_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doubly stochastic (CDS) maps acting on $XA$. We introduce the notion of symmetric distinguishability of an elementary source and prove that it is a monotone under both these classes of free operations. We study the tasks of distillation and dilution of symmetric distinguishability, both in the one-shot and asymptotic regimes. We prove that in the asymptotic regime, the optimal rate of converting one elementary source to another is equal to the ratio of their quantum Chernoff divergences, under both these classes of free operations. This imparts a new operational interpretation to the quantum Chernoff divergence. We also obtain interesting operational interpretations of the Thompson metric, in the context of the dilution of symmetric distinguishability.

中文翻译:

对称可区分性作为量子资源

我们建立了对称可区分性的资源理论,其基本对象是基本量子信息源,即以给定的先验概率发射两种可能的量子态之一的源。这样的源可以用复合系统$ XA $的古典量子状态表示,对应于两个量子态的集合,其中$ X $是古典的,而$ A $是量子。我们研究了两种不同类型的自由操作的资源理论:$(i)$ $ {\ rm {CPTP}} _ A $,它由仅作用于$ A $的量子通道和$(ii)$有条件的双随机变量组成(CDS)地图作用于$ XA $。我们介绍了基本源的对称可区分性的概念,并证明了这两种自由操作类别下它都是单调的。我们研究了单次和渐进两种情况下蒸馏和稀释对称可分辨性的任务。我们证明,在两种自由操作类别下,在渐近状态下,将一个基本源转换为另一基本源的最佳速率等于其量子Chernoff发散的比率。这为量子切尔诺夫发散量提供了新的运算解释。在对称可分辨性的稀释范围内,我们还获得了汤普森度量的有趣的操作解释。这为量子切尔诺夫发散量提供了新的运算解释。在对称可分辨性的稀释范围内,我们还获得了汤普森度量的有趣的操作解释。这为量子切尔诺夫发散量提供了新的运算解释。在对称可分辨性的稀释范围内,我们还获得了汤普森度量的有趣的操作解释。
更新日期:2021-02-26
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