Entropic uncertainty relations for multiple measurements

TL;DR

This paper derives concise entropic uncertainty relations for multiple quantum measurements, applicable with or without quantum memory, unifying and extending previous two-measurement results relevant to quantum foundations and cryptography.

Contribution

It introduces a unified method to derive entropic uncertainty relations for multiple measurements, generalizing known two-measurement relations and applicable to quantum cryptography.

Findings

Relations are concise and easy to compute.

Recover known relations for two observables.

Applicable to quantum cryptography protocols.

Abstract

We present the entropic uncertainty relations for multiple measurement settings in quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory. They take concise forms which can be proven in a unified method and easy to calculate. Our results recover the well known entropic uncertainty relations for two observables, which show the uncertainties about the outcomes of two incompatible measurements. Those uncertainty relations are applicable in both foundations of quantum theory and the security of many quantum cryptographic protocols.