Generalised entropy accumulation

Understand

Consider a sequential process in which each step outputs a system $A_i$ and updates a side information register $E$.

• We prove that if this process satisfies a natural "non-signalling" condition between past outputs and future side information, the min-entropy of the outputs $A_1, \dots, A_n$ conditioned on the side information $E$ at the end of the process can be bounded from below by a sum of von Neumann entropies associated with the individual steps.
• This is a generalisation of the entropy accumulation theorem (EAT), which deals with a more restrictive model of side information: there, past side information cannot be updated in subsequent rounds, and newly generated side information has to satisfy a Markov condition.
• Due to its more general model of side-information, our generalised EAT can be applied more easily and to a broader range of cryptographic protocols.