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 md5=f9007b104c3add9b55801c7ca7f6e76d" 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 md5=8a1f7b62f1e129dc47a24a8475ca94a4" title="Click to view the MathML source">Φ:A→B is a tracial positive linear map between md5=f9007b104c3add9b55801c7ca7f6e76d" title="Click to view the MathML source">C⁎-algebras, md5=3b4aee1b2704f8ec04f9dbcb8de633be" title="Click to view the MathML source">ρ∈A is a Φ-density element and md5=dbed8a1072cb05337894b69eb53bc605" title="Click to view the MathML source">A,B are self-adjoint operators of md5=1ff0654e956a78c29dce004b7de59916" title="Click to view the MathML source">A such that md5=25e7c2cb63b6bac84c54935d71534d76"> for some scalers md5=050285b7163f300282cd833edf6cda8a" title="Click to view the MathML source">0<m<M, then under some conditions
where md5=fadfd7d5195c31aa50f144cfd5c662ae" title="Click to view the MathML source">Km,M(ρ[A,B]) is the Kantorovich constant of the operator md5=61bcfc5c79430e8681c00e84548eedd4"> and md5=0ac858277be6d30b24f2d5a03d40cfbb" 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.