Entanglement sampling and applications

TL;DR

This paper introduces a new tool for analyzing how min-entropy, a measure of quantum entanglement, behaves under various processes, with applications in quantum cryptography, decoupling, and uncertainty relations.

Contribution

It presents a generic method to relate post-process min-entropy to the original, enabling new bounds and results in quantum information theory.

Findings

New upper bounds on quantum random access codes

Existence of local decouplers demonstrated

High-order entropic uncertainty relations established

Abstract

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 sampling results lead to new upper bounds on quantum random access codes, and imply the existence of "local decouplers". 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.