Yet Another Proof of the Joint Convexity of Relative Entropy

DOI10.1007/S11005-022-01562-XarXiv2112.13763WikidataQ113900758 ScholiaQ113900758MaRDI QIDQ6386801

Mary Beth Ruskai

Publication date: 27 December 2021

Abstract: The joint convexity of the map $(X,A)mapsto{X}^{*}{A}^{-1}X$, an integral representation of operator convex functions, and an observation of Ando are used to obtain a simple proof of both the joint convexity of relative entropy and a trace convexity result of Lieb. The latter was the key ingredient in the original proof of the strong subadditivity of quantum entropy.

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Measures of information, entropy (94A17) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Quantum entropies (81P17)

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