刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:1 March 2017
年:2017
卷:447
期:1
页码:666-680
全文大小:350 K
文摘
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 Φ:A→B is a tracial positive linear map between C⁎-algebras, aee1b2704f8ec04f9dbcb8de633be" title="Click to view the MathML source">ρ∈A is a Φ-density element and A,B are self-adjoint operators of A such that ac84c54935d71534d76"> for some scalers 0<m<M, then under some conditions
equation(0.1)
where ae" title="Click to view the MathML source">Km,M(ρ[A,B]) is the Kantorovich constant of the operator and ac858277be6d30b24f2d5a03d40cfbb" title="Click to view the MathML source">Vρ,Φ(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 generalized Wigner–Yanase–Dyson skew information.