Sandwiched Renyi量子相对熵单调性的另一证明  

A new proof for monotonicity of sandwiched Renyi relative entropy

作　　者：王友乐[1,2] 罗懋康 邓科[1] WANG You-Le1＇2 , LUO Mao-Kang1 , DENG Ke1(1. College of Mathematics, Sichuan University, Chengdu 610064, China~ 2. Science and Technology on Electronic Information Control Laboratory, Chengdu 610000, Chin)

机构地区：[1]四川大学数学学院,成都610064 [2]电子信息控制重点实验室,成都610000

出　　处：《四川大学学报（自然科学版）》2018年第2期257-259,共3页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11301361)

摘　　要：量子相对熵在保迹完全正定的映射作用下是单调递减的.此外,对于一种新提出的Sandwiched Renyi量子相对熵,当映射满足Schwarz不等式或映射保迹正定时,也有研究证明该量子相对熵的单调性也成立.本文利用复插值技巧给出当α∈[1/2,1)时Sandwiched Renyi量子相对熵单调性的另一证明.该技巧曾被用于证明α∈(1,∞)时量子相对熵在保迹正定映射的作用下满足单调性.It is well known that quantum relative entropy is monotonically decreasing under the complete- ly positive and trace-preserving maps. For a new proposed sandwiched Renyi quantum relative entropy, the monotonicity still holds under the linear trace-preserving map whose Hilber-Schmidt adjoint map sat- isfies Schwarz inequality. In this paper, we give a new proof for the monotonicity of the sandwiched Re- 1 nyi relative entropy for a α∈[1/2,1）The proof is based on the complex interpolation techniques, which is used to prove the monotonicity under the trace-preserving and positive map for α∈（1,∞）.

关 键 词：Sandwiched Renyi量子相对熵 单调性 复插值技巧 

分 类 号：O29[理学—应用数学]