Symmetric distinguishability as a quantum resource
Symmetric distinguishability as a quantum resource
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DOI：
10.1088/1367-2630/ac14aa
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发表时间：
2021-02
影响因子：
3.3
通讯作者：
Robert Salzmann;N. Datta;G. Gour;Xin Wang;M. Wilde
中科院分区：
文献类型：
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作者：
Robert Salzmann;N. Datta;G. Gour;Xin Wang;M. Wilde
我们发展了一种对称可区分性的资源理论，其基本对象是基本量子信息源，即在给定先验概率下发射两种可能量子态之一的源。这样的源可以用复合系统 XA 的经典量子态来表示，对应于两个量子态的系综，其中 X 是经典态，A 是量子态。我们研究两类不同类型的自由操作的资源理论：（i）CPTP A，它由仅作用于 A 的量子通道组成，以及（ii）作用于 XA 的条件双随机映射。我们引入了基本源的对称可区分性的概念，并证明它在这两类自由运算下都是单调的。我们研究一次性和渐近机制中对称可区分性的蒸馏和稀释任务。我们证明，在渐近状态下，在这两类自由运算下，将一种基本源转换为另一种基本源的最佳速率等于它们的量子切尔诺夫散度之比。这为量子切尔诺夫散度提供了新的操作解释。在对称可区分性稀释的背景下，我们还获得了汤普森度量的有趣的操作解释。
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) CPTP A , which consists of quantum channels acting only on A, and (ii) conditional doubly stochastic 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.