Quantum information inequalities via tracial positive linear maps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:447

Article

Dadkhah, Ali¹  Moslehian, Mohammad Sal¹ 

[1] Ferdowsi Univ Mashhad, Dept Pure Math, CEAAS, POB 1159, Mashhad 91775, Iran

关键词: Tracial positive linear map;    Heisenberg uncertainty relation;    Generalized covariance;    Generalized correlation;    Generalized Wigner-Yanase skew information;    C*-algebra;   

DOI  :  10.1016/j.jmaa.2016.10.027

来源: Elsevier

【 摘 要 】

We present some generalizations of quantum information inequalities involving tracial positive linear maps between C*-algebras. Among several results, we establish a noncommutative Heisenberg uncertainty relation. More precisely, we show that if Phi : A -> B is a tracial positive linear map between C*-algebras, rho is an element of A is a Phi-density element and A, B are self-adjoint operators of A such that sp(-i rho(1/2)[A, B]rho(1/2)) subset of [m, M] for some scalers 0 < m < M, then under some conditions V-rho, Phi(A)#V-rho,Phi(B) >= 1/2 root K-m,K- M(rho[A, B]) vertical bar Phi,(rho[A, B])vertical bar, (0.1) where K-m,K-M(rho[A,B]) is the Kantorovich constant of the operator -i rho(1/2)[A, B]rho(1/2) and V-rho,V-Phi(X) is the generalized variance of X. In addition, we use some arguments differing from the scalar theory to present some inequalities related to the generalized correlation and the generalised Wigner-Yanase-Dyson skew information. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free