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, dbcb8de633be" title="Click to view the MathML source">ρ∈A is a Φ-density element and dbed8a1072cb05337894b69eb53bc605" title="Click to view the MathML source">A,B are self-adjoint operators of A such that for some scalers 0<m<M, then under some conditions
equation(0.1)
where Km,M(ρ[A,B]) is the Kantorovich constant of the operator and 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.