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 9dc47a24a8475ca94a4" 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, aee1b2704f8ec04f9dbcb8de633be" title="Click to view the MathML source">ρ∈A is a Φ-density element and bed8a1072cb05337894b69eb53bc605" title="Click to view the MathML source">A,B are self-adjoint operators of e956a78c29dce004b7de59916" title="Click to view the MathML source">A such that e7c2cb63b6bac84c54935d71534d76">85" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16306230-si6.gif"> for some scalers 85b7163f300282cd833edf6cda8a" title="Click to view the MathML source">0<m<M, then under some conditions
where ae" title="Click to view the MathML source">Km,M(ρ[A,B]) is the Kantorovich constant of the operator and 858277be6d30b24f2d5a03d40cfbb" 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.