The Wigner–Araki–Yanase theorem and the quantum resource theory of asymmetry

Abstract

The WAY theorem establishes an important constraint that conservation laws\nimpose on quantum mechanical measurements. We formulate the WAY theorem in the\nbroader context of resource theories, where one is constrained to a subset of\nquantum mechanical operations described by a symmetry group. Establishing\nconnections with the theory of quantum state discrimination we obtain optimal\nunitaries describing the measurement of arbitrary observables, explain how\nprior information can permit perfect measurements that circumvent the WAY\nconstraint, and provide a framework that establishes a natural ordering on\nmeasurement apparatuses through a decomposition into asymmetry and charge\nsubsystems.\n