关于Wigner-Yanase-Dyson斜信息的不等式  

Inequalities of Wigner-Yanase-Dyson Skew Information

作　　者：范亚静 曹怀信[2] FAN YAJING;CAO HUAIXIN(College of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China;College of Mathematics and Information Science, Shaanxi Normal University, Xi＇an 710062, China;College of Mathematics and Information Science, Shaanxi Normal University, Xi＇an 710062, China)

机构地区：[1]北方民族大学数学与信息科学学院,银川750021 [2]陕西师范大学数学与信息科学学院,西安710062

出　　处：《应用数学学报》2017年第6期849-861,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11701011;11371012)资助项目

摘　　要：Wigner-Yanase-Dyson(WYD)斜信息量化的是可观测量与非交换的守恒量之间的信息内容,并推广了Wigner和Yanase提出的斜信息.首先我们分别给出两个例子说明WYD斜信息的超可加性和相关的不等式—般情况下不成立,并建立WYD斜信息的超可加性的两个弱形式,称之为弱超可加性.此外,我们还证明关于量子-经典态和经典-量子态的WYD斜信息的不等式成立.The Wigner-Yanase-Dyson （WYD） skew information quantifies the amount of information on the values of observable not commuting with the conserved quantity, and extends the skew information introduced by Wigner and Yanase. We observe first that the superadditivity and a related inequality for the WYD skew information are not valid generally by using two examples, respectively, and then establish two weak forms of the superadditivity of the WYD skew information, called the weak superadditivity. Moreover, we prove the related inequality for WYD skew information holds for all quantum-classical or classical-quantum states.

关 键 词：量子态 Wigner—Yanase—Dyson斜信息 可观测量 

分 类 号：O177.1[理学—数学]