Weight of informativeness, state exclusion games and excludible information

TL;DR

This paper introduces a weight-based measure of measurement informativeness in quantum resource theory, linking it to quantum state exclusion and establishing a new correspondence with excludible information, with potential broad applicability.

Contribution

It proposes a novel weight-based quantifier of measurement informativeness and connects it to quantum state exclusion and excludible information, expanding the understanding of quantum resource theories.

Findings

The weight of informativeness precisely captures measurement advantage in state exclusion.

For quantum-to-classical channels, excludible information equals the weight of informativeness.

A new three-way correspondence is established between quantifiers, exclusion games, and information measures.

Abstract

We consider the quantum resource theory of measurement informativeness and introduce a weight-based quantifier of informativeness. We show that this quantifier has operational significance from the perspective of quantum state exclusion, by showing that it precisely captures the advantage a measurement provides in minimising the error in this game. We furthermore introduce information theoretic quantities related to exclusion, in particular the notion of excludible information of a quantum channel, and show that for the case of quantum-to-classical channels it is determined precisely by the weight of informativeness. This establishes a three-way correspondence which sits in parallel to the recently discovered correspondence in quantum resource theories between robustness-based quantifiers, discrimination games, and accessible information. We conjecture that the new correspondence between a weight-based quantifier and an exclusion-based task found in this work is a generic correspondence that holds in the context of quantum resource theories.