Entropic Bounds as Uncertainty Measure of Unitary Operators

TL;DR

This paper introduces an entropic uncertainty relation for pairs of unitary operators, linking their distinguishability and incompatibility to mutually unbiased bases within a guessing game framework.

Contribution

It reformulates uncertainty for unitary operators using entropic measures and connects maximal incompatibility to mutually unbiased bases, providing new insights into operator distinguishability.

Findings

Derived an entropic uncertainty relation for unitary operators

Linked maximal incompatibility to mutually unbiased bases

Showed compatibility of distinguishable operators

Abstract

We reformulate the notion of uncertainty of pairs of unitary operators within the context of guessing games and derive an entropic uncertainty relation for a pair of such operators. We show how distinguishable operators are compatible while maximal incompatibility of unitary operators can be connected to bases for some subspace of operators which are mutually unbiased.