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We introduce a way of quantifying how informative a quantum measurement is,starting from a resource-theoretic perspective. This quantifier, which we callthe robustness of measurement, describes how much `noise' must be added to ameasurement before it becomes completely uninformative. We show that thisgeometric quantifier has operational significance in terms of the advantage themeasurement provides over guessing at random in an suitably chosen statediscrimination game. We further show that it is the single-shot generalisationof the accessible information of a certain quantum-to-classical channel. Usingthis insight, we also show that the recently-introduced robustness of coherenceis the single-shot generalisation of the accessible information of an ensemble.Finally we discuss more generally the connection between robustness-basedmeasures, discrimination problems and single-shot information theory.

Robustness of Measurement, discrimination games and accessible information