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Séminaire de Probabilités commun ICJ/UMPA

Entropy accumulation

by Omar Fawzi (ENS Lyon)

jeudi 27 avril 2017 de au (Europe/Paris)
at UMPA ( salle 435 )
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. The analysis of a large system can hence be
reduced to the study of its parts. This is relevant for applications
in particular to quantum cryptography.