Quantum information inequalities via tracial positive linear maps

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• 作者：Ali Dadkhah ^{dadkhah61@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Mohammad Sal Moslehian ; ^{moslehian@um.ac.ir" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Tracial positive linear map ; Heisenberg uncertainty relation ; Generalized covariance ; Generalized correlation ; Generalized Wigner&ndash ; Yanase skew information ; C⁎C⁎-algebra
• 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 w the MathML source">C^⁎-algebras. Among several results, we establish a noncommutative Heisenberg uncertainty relation. More precisely, we show that if w the MathML source">Φ:A→B is a tracial positive linear map between w the MathML source">C^⁎-algebras, w the MathML source">ρ∈A is a Φ-density element and w the MathML source">A,B are self-adjoint operators of w the MathML source">A such that w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306230&_mathId=si6.gif&_user=111111111&_pii=S0022247X16306230&_rdoc=1&_issn=0022247X&md5=25e7c2cb63b6bac84c54935d71534d76">lineImage" height="20" width="185" 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 w the MathML source">0<m<M, then under some conditions where w the MathML source">K_m,M(ρ[A,B]) is the Kantorovich constant of the operator w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306230&_mathId=si10.gif&_user=111111111&_pii=S0022247X16306230&_rdoc=1&_issn=0022247X&md5=61bcfc5c79430e8681c00e84548eedd4">lineImage" height="20" width="88" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16306230-si10.gif"> and w the MathML source">V_ρ,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.