International Association
for Cryptologic Research

A natural measure for the amount of quantum information that a physical system $E$ holds about another system $A = A_1,...,A_n$ is given by the min-entropy $\\hmin(A|E)$. Specifically, the min-entropy measures the amount of entanglement between $E$ and $A$, and is the relevant measure when analyzing a wide variety of problems ranging from randomness extraction in quantum cryptography, decoupling used in channel coding, to physical processes such as thermalization or the thermodynamic work cost (or gain) of erasing a quantum system. As such, it is a central question to determine the behaviour of the min-entropy after some process M is applied to the system $A$. Here we introduce a new generic tool relating the resulting min-entropy to the original one, and apply it to several settings of interest, including sampling of subsystems and measuring in a randomly chosen basis.

The results on random measurements yield new high-order entropic uncertainty relations with which we prove the optimality of cryptographic schemes in the bounded quantum storage model. This is an abridged version of the paper; the full version containing all proofs and further applications can be found in \\cite{DFW13}.