Entropic uncertainty relations and the stabilizer formalism

TL;DR

This paper explores entropic uncertainty relations within the stabilizer formalism, demonstrating tight bounds for stabilizer bases and comparing different uncertainty measures for specific observables.

Contribution

It applies the stabilizer formalism to derive tight entropic uncertainty bounds and compares various uncertainty relations for dichotomic anticommuting observables.

Findings

Maassen-Uffink relation is tight for stabilizer bases

Entropic bounds are optimal for stabilizer measurements

Variance-based and entropic relations differ in strength for certain observables

Abstract

Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the characterization of observables that allow strong uncertainty relations, and the construction of such relations for the case of several observables. We demonstrate how the stabilizer formalism can be applied to these questions. We show that the Maassen-Uffink entropic uncertainty relation is tight for the measurement in any pair of stabilizer bases. We compare the relative strengths of variance-based and various entropic uncertainty relations for dichotomic anticommuting observables.