QMATH/GAMP Lecture: Entropy accumulation – University of Copenhagen

QMath > Events > Quantum Lunch > w 6 Frédéric Dupuis

QMATH/GAMP Lecture: Entropy accumulation

Speaker: Frédéric Dupuis from Masaryk University, Czech Republic 

Title: Entropy accumulation

We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an n-partite system A = (A_1,..., A_n) corresponds to the sum of the entropies of its parts A_i. The  Asymptotic Equipartition Property implies that this is indeed the case to first order in n --- under the assumption that the parts A_i 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 A_i 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 device-independent cryptography, for instance, the approach yields essentially optimal security bounds valid for general attacks, as shown by Arnon-Friedman et al.