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We consider the quantum resource theory of measurement informativeness andintroduce a weight-based quantifier of informativeness. We show that thisquantifier has operational significance from the perspective of quantum stateexclusion, by showing that it precisely captures the advantage a measurementprovides in minimising the error in this game. We furthermore introduceinformation theoretic quantities related to exclusion, in particular the notionof excludible information of a quantum channel, and show that for the case ofquantum-to-classical channels it is determined precisely by the weight ofinformativeness. This establishes a three-way correspondence which sits inparallel to the recently discovered correspondence in quantum resource theoriesbetween robustness-based quantifiers, discrimination games, and accessibleinformation. We conjecture that the new correspondence between a weight-basedquantifier and an exclusion-based task found in this work is a genericcorrespondence that holds in the context of quantum resource theories.

Weight of informativeness, state exclusion games and excludible information