WAY beyond conservation laws

TL;DR

This paper reformulates and extends the Wigner-Araki-Yanase (WAY) theorem, broadening its scope from additive conservation laws to general quantum incompatibility and positive operator valued measures, thus revealing new measurement limitations.

Contribution

It introduces a new formulation of the WAY-theorem based on quantum incompatibility, removing previous assumptions of additivity and conservation, and extends it to POVMs.

Findings

Reformulation of WAY-theorem in terms of quantum incompatibility

Generalization to non-additive and non-conserved quantities

Extension to positive operator valued measures (POVMs)

Abstract

The ability to measure every quantum observable is ensured by a fundamental result in quantum measurement theory. Nevertheless, additive conservation laws associated with physical symmetries, such as the angular momentum conservation, may lead to restrictions on the measurability of the observables. Such limitations are imposed by the theorem of Wigner, Araki and Yanase (WAY). In this paper a new formulation of the WAY-theorem is presented rephrasing the measurability limitations in terms of quantum incompatibility. This broader mathematical basis enables us to both capture and generalise the WAY-theorem by allowing to drop the assumptions of additivity and even conservation of the involved quantities. Moreover, we extend the WAY-theorem to the general level of positive operator valued measures.