A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy

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dc.creatorCarlen, Eric A.
dc.creatorLieb, Elliott H.
dc.date2007-01-12
dc.date.accessioned2026-07-07T07:40:38Z
dc.date.available2026-07-07T07:40:38Z
dc.descriptionWe 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<p\le 1 and convex for p=2. We then derive from this a Minkowski type inequality for operators on a tensor product of three Hilbert spaces, and show how this implies the strong subadditivity of quantum mechanical entropy. For p>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.
dc.description13 pages, plaintex, dedicated to M. Birman
dc.identifierhttps://arxiv.org/abs/math/0701352
dc.identifierhttp://arxiv.org/abs/math/0701352
dc.identifierAmerican Mathematical Society Translations, series 2, vol 189, pp. 59-69 (1999)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121832
dc.subjectOperator Algebras
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subjectQuantum Physics
dc.subject47A63, 15A90
dc.titleA Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy
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