Robustness of Measurement, Discrimination Games, and Accessible Information

We introduce a resource theory of measurement informativeness. This allows us to define an associated quantifier, which we call the robustness of measurement. It describes how much “noise” must be added to a measurement before it becomes completely uninformative. We show that this geometric quantifier has operational significance in terms of the advantage the measurement provides over guessing at random in a suitably chosen state discrimination game and that it is the single-shot generalization of the accessible information of a certain quantum-to-classical channel. Using this insight, we further show that the recently introduced robustness of asymmetry or coherence is the single-shot generalization of the accessible information of an ensemble. Finally, we discuss more generally the connection between robustness-based measures, discrimination problems, and information-theoretic quantities.

Figure 1

Triangle of associations found here. A robustness-based measure is found to give the optimal advantage in a suitably chosen discrimination game. This, in turn, is found to be equivalent to a suitably defined information-theoretic quantity—the single-shot accessible information of a suitably defined channel. It is interesting to ask how general this triangle of associations is.