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Physical Review A

Alternative formulation of the Wigner-Araki-Yanase theorem

Kiyotaka Kakazu, Saverio Pascazio

Published May 1, 1995• 8 citations
Publisher

Abstract

We study the Wigner-Araki-Yanase theorem by utilizing a slightly modified version of a formulation recently proposed by Ozawa [Phys. Rev. Lett. 67, 1950 (1991)]. After characterizing the quantities that are conserved in the evolution of the total system (object plus apparatus), we suitably decompose the Hamiltonian and show that the Wigner-Araki-Yanase theorem can be formulated in terms of the conserved quantities of the object system and of some observables of the apparatus. A few examples clarify our general arguments.

DOI
10.1103/physreva.51.3469

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We study the Wigner-Araki-Yanase theorem by utilizing a slightly modified version of a formulation recently proposed by Ozawa [Phys. Rev. Lett. 67, 1950 (1991)]. After characterizing the quantities that are conserved in the evolution of the total system (object plus apparatus), we suitably decompose the Hamiltonian and show that the Wigner-Araki-Yanase theorem can be formulated in terms of the conserved quantities of the object system and of some observables of the apparatus. A few examples clarify our general arguments.
Abstract We present a novel interpretation of the Wigner-Araki-Yanase (WAY) theorem based on a relational view of quantum mechanics. Several models are analysed in detail, backed up by general considerations, which serve to illustrate that the moral of the WAY theorem may be that in the presence of symmetry, a measuring apparatus must fulfil the dual purpose of both reflecting the statistical behaviour of the system under investigation, and acting as a physical reference system serving to define those quantities which must be understood as relative.
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.