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 e76d" title="Click to view the MathML source">C⁎-algebras. Among several results, we establish a noncommutative Heisenberg uncertainty relation. More precisely, we show that if a8475ca94a4" title="Click to view the MathML source">Φ:A→B is a tracial positive linear map between e76d" title="Click to view the MathML source">C⁎-algebras, b4aee1b2704f8ec04f9dbcb8de633be" title="Click to view the MathML source">ρ∈A is a Φ-density element and 894b69eb53bc605" title="Click to view the MathML source">A,B are self-adjoint operators of A such that e7c2cb63b6bac84c54935d71534d76"> for some scalers a8a" title="Click to view the MathML source">0<m<M, then under some conditions
where Km,M(ρ[A,B]) is the Kantorovich constant of the operator e8681c00e84548eedd4"> and e6d30b24f2d5a03d40cfbb" 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.