Superadditivity of Wigner-Yanase-Dyson information revisited
Superadditivity of Wigner-Yanase-Dyson information revisited
复制标题
重新审视 Wigner-Yanase-Dyson 信息的超可加性
DOI：
10.1007/s10955-008-9534-y
复制
发表时间：
2008-06-01
影响因子：
1.6
通讯作者：
Zhang, Qiang
中科院分区：
文献类型：
--
作者：
Luo, Shunlong;Zhang, Qiang
Wigner-Yanase-Dyson信息是量子Fisher信息的一个重要变体。关于Wigner和Yanase最初提出的信息内容概念的两个基本要求是凸性和超可加性。前者在1973年由Lieb完全建立，并导致了量子熵强次可加性的第一个证明。后者虽然被广泛认为是正确的，但最近被汉森推翻了。然而，在两种极端情况下，即纯态或经典态，也建立了超可加性。在本文中，我们首先回顾了一种将二分态分类为经典态、半量子态和量子态的方案，这些状态按量子量增加的顺序排列。然后证明了所有半量子态的Wigner-Yanase-Dyson信息的超可加性。Wigner-Yanase-Dyson信息的凸性在这里起着至关重要的作用。
The Wigner-Yanase-Dyson information is an important variant of quantum Fisher information. Two fundamental requirements concerning this notion of information content originally postulated by Wigner and Yanase are convexity and superadditivity. The former was fully established by Lieb in 1973, and led to the first proof of the strong subadditivity of quantum entropy. The latter, although widely believed to be true, was quite recently disproved by Hansen. Nevertheless, superadditivity has also been established in two extreme cases, i.e., when the states are pure or classical. In this paper, we first review a scheme to classify bipartite states into a hierarchy of classical, semi-quantum, and quantum states, which are arranged in the order of increasing quantumness. We then prove the superadditivity of the Wigner-Yanase-Dyson information for all semi-quantum states. The convexity of the Wigner-Yanase-Dyson information plays a crucial role here.