A Resource Theory of Quantum Measurements

Abstract

Resource theories are broad frameworks that capture how useful objects are in performing specific tasks. In this paper we devise a formal resource theory quantum measurements, focusing on the ability of a measurement to acquire information. The objects of the theory are equivalence classes of positive operator-valued measures (POVMs), and the free transformations are changes to a measurement device that can only deteriorate its ability to report information about a physical system. We show that catalysis and purification, protocols that are possible in other resource theories, are impossible in our resource theory for quantum measurements. Standard measures of information gain are shown to be resource monotones, and the resource theory is applied to the task of quantum state discrimination.

13 pages, 1 figure, 3 appendices

References in corpus (14)

• Quantum Resource Theories
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• Clean Positive Operator Valued Measures
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• Every quantum helps: Operational advantage of quantum resources beyond convexity
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• Directly Characterizing the Coherence of Quantum Detectors by Sequential Measurement
• Order preserving maps on quantum measurements
• Completeness Stability of Quantum Measurements
• Entropic partial orderings of quantum measurements
• Multi-object operational tasks for measurement incompatibility
• Detector entanglement: Quasidistributions for Bell-state measurements
• Entropic and operational characterizations of dynamic quantum resources
• Infinite dimensionality of the post-processing order of measurements on a general state space
• Impact of quadrature measurement on quantum coherence
• Distance-based measures and Epsilon-measures for measurement-based quantum resources