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.
翻译:我们开发了一种对称区别的资源理论,其基本目标为基本量信息源,即排放两个可能的量子状态之一的源,并给出了先前的概率。这种源可以是合成系统美元XA$的古典-量状状态,相当于两个量状的组合,美元为经典美元,美元为定量。我们研究两种不同类别自由操作的资源理论:美元(一)美元(美元)和美元(CPTP)A$(美元),它由量子渠道组成,仅以美元为单位,美元(二)是有条件的双对称状态(CDS)地图,以美元为单位。我们引入了一个基本源的对称式区别概念,并证明它是两个类别自由操作的单数。我们研究的是两种不同的自由操作的精度分辨和分辨区分任务,在一发和亚质制度中,我们证明在定量的量量度机制中,将一种基本值的可辨度的可辨度比值转化为另一种可辨度的操作源码。我们研究的是,在深度解释中,将一种基本水平的可辨度的可辨度的可辨度的操作性比值转换度与另一种可辨度,在一种可辨度上,这种可辨误判分度的精确度的精确度的计算。