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Résumé |
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. In this talk, I will 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. I will also show a generalization of this result
to relative entropies
and will illustrate the result with an application to quantum cryptography.
Based on https://arxiv.org/abs/1607.01796, https://arxiv.org/abs/1909.05826 |
