Entropic bounds as uncertainty measure of unitary operators

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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

We reformulated the notion of uncertainty for pairs of unitary operators in the context of guessing games and derived an entropic uncertainty relation for such pairs. We demonstrated the compatibility of distinguishable operators and connected maximal incompatibility of unitary operators to bases for some subspace of mutually unbiased operators.