Wigner-Araki-Yanase theorem 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.⋆ Dedicated to my beloved daughter Minttu; may your life be full of joy and wonder.

Measurement disturbance and conservation laws in quantum mechanics

“…For instance, there are obstacles to the implementation of quantum logic gates [6][7][8]. The theorem continues to inspire research in a variety of directions (some recent examples are [9][10][11][12][13][14][15]), and connections have been made to other fields of research; for instance in the resource theories of asymmetry [16] and coherence [17,18], the theory of quantum reference frames [19], quantum clocks [20], and quantum thermodynamics [21][22][23][24][25]. Despite this ongoing development, the full scope of the WAY theorem is not known; particularly, the role of disturbance has not yet been carefully examined.…”