Robustness of Measurement, discrimination games and accessible information

Understand

We introduce a way of quantifying how informative a quantum measurement is, starting from a resource-theoretic perspective.

• This quantifier, which we call the robustness of measurement, 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 an suitably chosen state discrimination game.
• We further show that it is the single-shot generalisation of the accessible information of a certain quantum-to-classical channel.