RIGHT MEAN FOR THEα-z BURES-WASSERSTEIN QUANTUM DIVERGENCE  

作　　者：Miran JEONG Jinmi HWANG Sejong KIM 

机构地区：[1]Department of Mathematics,Chungbuk National University,Cheongju 28644,Korea [2]Department of Mathematics,Sungkyunkwan University,Suwon 16419,Korea

出　　处：《Acta Mathematica Scientia》2023年第5期2320-2332,共13页数学物理学报（B辑英文版）

基　　金：supported by the National Re-search Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(NRF-2022R1A2C4001306);supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2022R1I1A1A01068411)。

摘　　要：The optimization problem to minimize the weighted sum ofα-z Bures-Wasserstein quantum divergences to given positive definite Hermitian matrices has been solved.We call the unique minimizer theα-z weighted right mean,which provides a new non-commutative version of generalized mean(H?lder mean).We investigate its fundamental properties,and give many interesting operator inequalities with the matrix power mean including the Cartan mean.Moreover,we verify the trace inequality with the Wasserstein mean and provide bounds for the Hadamard product of two right means.

关 键 词：Rényi relative entropy Bures-Wasserstein quantum divergence right mean power mean Cartan mean Wasserstein mean 

分 类 号：O177[理学—数学]