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 without an independence assumption, provided one quantifies the uncertainty about the individual systems Ai by the von Neumann entropy of suitably chosen conditional states. This has applications in cryptography: for example, it can be used to generically reduce the security of QKD in the general attack, finite-key regime to the case of iid attacks in the asymptotic key regime. It can also be used in the device-independent setting to provide essentially optimal security bounds, as shown by Arnon-Friedman, Renner and Vidick. Joint work with Frederic Dupuis and Renato Renner, available https://arxiv.org/abs/1607.01796.