Resource theory of asymmetric distinguishability
Resource theory of asymmetric distinguishability
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DOI：
10.1103/physrevresearch.1.033170
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发表时间：
2019-05
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影响因子：
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通讯作者：
Xin Wang;M. Wilde
中科院分区：
文献类型：
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作者：
Xin Wang;M. Wilde
本文系统地发展了大约十年前提出的非对称可分配性资源理论[K。松本，arXiv：1010.1030（2010）]。这种资源理论的关键组成部分是量子盒，由一对量子态组成，可以通过任意量子通道免费操纵。我们引入比特的非对称可互换性作为这个资源理论的基本货币，并证明了它是一个可逆的资源理论在渐近极限，量子相对熵是资源相互转换的基本速率。量子盒是由独立同分布（i.i.d.）可以将状态转换为非对称可重构性的比特，并且可重构性代价是用于逆变换的最优速率。这两个量都等于量子相对熵。精确的一次可重复性等于最小相对熵，精确的一次可重复性代价等于最大相对熵。推广这些结果，近似一次可压缩性等于光滑最小相对熵，近似一次可压缩性代价等于光滑最大相对熵。作为前面结果的一个显著应用，我们证明了从一对独立同分布的最优渐近转换率。量子态转换成另一对独立同分布的量子态完全由它们的量子相对熵的比值来表征。
This paper systematically develops the resource theory of asymmetric distinguishability, as initiated roughly a decade ago [K. Matsumoto, arXiv:1010.1030 (2010)]. The key constituents of this resource theory are quantum boxes, consisting of a pair of quantum states, which can be manipulated for free by means of an arbitrary quantum channel. We introduce bits of asymmetric distinguishability as the basic currency in this resource theory, and we prove that it is a reversible resource theory in the asymptotic limit, with the quantum relative entropy being the fundamental rate of resource interconversion. The distillable distinguishability is the optimal rate at which a quantum box consisting of independent and identically distributed (i.i.d.) states can be converted to bits of asymmetric distinguishability, and the distinguishability cost is the optimal rate for the reverse transformation. Both of these quantities are equal to the quantum relative entropy. The exact one-shot distillable distinguishability is equal to the min-relative entropy, and the exact one-shot distinguishability cost is equal to the max-relative entropy. Generalizing these results, the approximate one-shot distillable distinguishability is equal to the smooth min-relative entropy, and the approximate one-shot distinguishability cost is equal to the smooth max-relative entropy. As a notable application of the former results, we prove that the optimal rate of asymptotic conversion from a pair of i.i.d. quantum states to another pair of i.i.d. quantum states is fully characterized by the ratio of their quantum relative entropies.