Robustness of Measurement, Discrimination Games, and Accessible Information

Area of Science:

• Quantum Information Science
• Quantum Measurement Theory
• Information Theory

Background:

• Quantifying the informativeness of quantum measurements is crucial for understanding quantum information processing.
• Existing measures often lack a clear operational meaning or a single-shot generalization.

Purpose of the Study:

• To introduce a resource theory for measurement informativeness.
• To define and analyze a new quantifier: the robustness of measurement.
• To establish connections between robustness measures, state discrimination, and information-theoretic quantities.

Main Methods:

• Development of a resource theory framework for measurement informativeness.
• Definition of the robustness of measurement as a geometric quantifier.
• Analysis of the operational significance in state discrimination games.
• Establishing connections to accessible information for quantum-to-classical channels and ensembles.

Main Results:

• The robustness of measurement quantifies the noise tolerance of an informative measurement.
• This quantifier provides an advantage over random guessing in specific state discrimination tasks.
• It is shown to be the single-shot generalization of accessible information for quantum-to-classical channels.
• Connections are established between robustness of asymmetry/coherence and accessible information of ensembles.

Conclusions:

• The robustness of measurement offers a powerful tool for characterizing quantum measurement informativeness.
• This work unifies concepts in quantum measurement, state discrimination, and information theory.
• The findings have potential applications in quantum communication and computation by providing a robust measure of information transfer.