A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy

Eric A. Carlen and Elliott H. Lieb
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Eric A. Carlen: Georgia Institute of Technology, School of Mathematics
Elliott H. Lieb: Princeton University, Departments of Mathematics and Physics

A chapter in Inequalities, 2002, pp 191-200 from Springer

Abstract: Abstract We consider the following trace function on n-tuples of positive operators: $${\Phi _P}({A_1},{A_2},...,{A_n}) = Tr({(\sum\limits_{j = 1}^n {A_j^P} )^{1/P}})$$ and prove that it is jointly concave for 0 2, Фp is neither convex nor concave. We conjecture that Фp is convex for 1

Keywords: Positive Operator; Operator Analog; Selfadjoint Operator; Partial Trace; National Science Foundation Grant (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55925-9_19

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DOI: 10.1007/978-3-642-55925-9_19

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