Wigner-Araki-Yanase theorem beyond conservation laws

Mikko Tukiainen
Phys. Rev. A 95, 012127 – Published 20 January 2017

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 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 generalize the WAY theorem by allowing us 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.

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  • Received 26 November 2016

DOI:https://doi.org/10.1103/PhysRevA.95.012127

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Mikko Tukiainen*

  • Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, 20500 Turku, Finland

  • *mikko.tukiainen@utu.fi

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Issue

Vol. 95, Iss. 1 — January 2017

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