How to Quantify a Dynamical Quantum Resource.
How to Quantify a Dynamical Quantum Resource.
复制标题
DOI：
10.1103/physrevlett.123.150401
复制
发表时间：
2019-06
影响因子：
8.6
通讯作者：
G. Gour;A. Winter
中科院分区：
文献类型：
--
作者：
G. Gour;A. Winter
我们表明，资源的相对熵从状态到通道的概括并不是唯一的，并且至少有六个这样的概括。然后，我们表明，这些推广的两个是渐近连续的，满足版本的渐近均分属性，和他们的正则化出现在幂指数通道版本的量子斯坦引理。为了获得我们的结果，我们使用了一种新的类型的“平滑”，可以应用于功能的通道（没有状态模拟）。我们称之为“自由平滑”，因为它允许在优化中进行更多的扩展。沿着的方式，我们表明，钻石范数可以表示为一个最大的相对熵距离的一组量子通道，并证明了各种性质的所有六个广义的相对熵的资源。
We show that the generalization of the relative entropy of a resource from states to channels is not unique, and there are at least six such generalizations. Then, we show that two of these generalizations are asymptotically continuous, satisfy a version of the asymptotic equipartition property, and their regularizations appear in the power exponent of channel versions of the quantum Stein's lemma. To obtain our results, we use a new type of "smoothing" that can be applied to functions of channels (with no state analog). We call it "liberal smoothing" as it allows for more spread in the optimization. Along the way, we show that the diamond norm can be expressed as a max relative entropy distance to the set of quantum channels, and prove a variety of properties of all six generalizations of the relative entropy of a resource.