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A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy

Eric A. Carlen·Elliott H. Lieb
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Abstract

We consider the following trace function on n-tuples of positive operators: Φ_p(A_1,A_2,...,A_n) = Trace (\sum_{j=1}^n A_j^p)^{1/p} and prove that it is jointly concave for 0 2, Φ_p is neither convex nor concave. We conjecture that Φ_p is convex for 1<p<2, but our methods do not show this.

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BibTeXRIS

Eric A. Carlen, Elliott H. Lieb. 2007-01-12. A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy. https://arxiv.org/abs/math/0701352

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