By Omar Fawzi (ENS Lyon)
Abstract: We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an n-partite system A=(A1,…An) corresponds to the sum of the entropies of its parts Ai. The Asymptotic Equipartition Property implies that this is indeed the case to first order in n, under the assumption that the parts Ai are identical and independent of each other. Here, we show that entropy accumulation occurs more generally, i.e., without an independence assumption, provided one quantifies the uncertainty about the individual systems Ai by the von Neumann entropy of suitably chosen conditional states. In this talk, I will introduce the more general framework and describe the main steps of the proof. Based on joint work with Frederic Dupuis and Renato Renner, most of it available in [ Ссылка ]

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