A resource theory of quantum measurements

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, 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.

Automated summary

The study focuses on formal resource theory of quantum measurements, showing that protocols like catalysis and purification are impossible in this theory. Standard measures of information gain are proven to be resource monotones, and the resource theory is applied to quantum state discrimination tasks.