WAY beyond conservation laws

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.