The WAY theorem and the quantum resource theory of asymmetry

TL;DR

This paper extends the WAY theorem within quantum resource theories, linking symmetry constraints to measurement limitations, and introduces a framework for optimal measurements and apparatus ordering based on asymmetry and charge subsystems.

Contribution

It generalizes the WAY theorem to resource theories, connects it with quantum state discrimination, and develops a framework for optimal measurements considering symmetry constraints.

Findings

Derived optimal unitaries for measuring arbitrary observables.

Showed how prior information enables perfect measurements bypassing the WAY constraint.

Established a natural ordering of measurement apparatuses via asymmetry decomposition.

Abstract

The WAY theorem establishes an important constraint that conservation laws impose on quantum mechanical measurements. We formulate the WAY theorem in the broader context of resource theories, where one is constrained to a subset of quantum mechanical operations described by a symmetry group. Establishing connections with the theory of quantum state discrimination we obtain optimal unitaries describing the measurement of arbitrary observables, explain how prior information can permit perfect measurements that circumvent the WAY constraint, and provide a framework that establishes a natural ordering on measurement apparatuses through a decomposition into asymmetry and charge subsystems.