Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Open Systems & Information Dynamics

Wigner-Araki-Yanase Theorem in General Theory of Quantum Measurement

Andrzej Łuczak

Published Sep 1, 2016• 3 citations
Publisher

Abstract

A general form of the Wigner-Araki-Yanase theorem is proved in the framework of quantum measurement theory based on the notion of instrument.
DOI
10.1142/s123016121650013x

Related papers

A relational perspective on the Wigner-Araki-Yanase theorem

Leon Loveridge

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.

arXiv:2006.07047•Journal of Physics Conference Series•Oct 1, 2020•14 citations

An Extension of the Wigner-Araki-Yanase Theorem to Multiplicative Conserved Quantities

Bernhard K. Meister

An extension of the Wigner-Araki-Yanase theorem to multiplicative conserved quantities is presented and approximate versions of the theorem are discussed.

arXiv:quant-ph/0701154•Jan 22, 2007•0 citations

A Reexamination of the Wigner and Araki-Yanase Theorem

S. Matsumoto

The limitation on the measurement of an operator imposed by the presence of one conservation law was discussed by Wigner and Araki-Yanase. But we do not know whether their results still hold or not when we consider two conservation laws or more at a time. In this article, a model of a quantum measuring process is discussed from the point of view that all three components of angular momentum should be conserved in the process.

Progress of Theoretical Physics•Jul 1, 1993•5 citations

UNCERTAINTY PRINCIPLE FOR QUANTUM INSTRUMENTS AND COMPUTING

Masanao Ozawa

The notion of quantum instruments is formalized as statistical equivalence classes of all the possible quantum measurements and mathematically characterized as normalized completely positive map valued measures under naturally acceptable axioms. Recently, universally valid uncertainty relations have been established to set a precision limit for any instruments given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to a quantitative generalization of the Wigner–Araki–Yanase theorem on the precision limit of measurements under conservation laws. Applying this, a rigorous lower bound is obtained for the gate error probability of physical implementations of Hadamard gates on a standard qubit of a spin 1/2 system by interactions with control fields or ancilla systems obeying the angular momentum conservation law.

arXiv:quant-ph/0310071•International Journal of Quantum Information•Dec 1, 2003•42 citations

Alternative formulation of the Wigner-Araki-Yanase theorem

Kiyotaka Kakazu, Saverio Pascazio

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.

Physical Review A•May 1, 1995•8 citations

Wigner-Araki-Yanase theorem and the realizability of quantum computing (Mathematical Study of Quantum Dynamical Systems and Its Application to Quantum Computer)

正直 小澤

数理解析研究所講究録•Jan 1, 2004•0 citations
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 notion of quantum instruments is formalized as statistical equivalence classes of all the possible quantum measurements and mathematically characterized as normalized completely positive map valued measures under naturally acceptable axioms. Recently, universally valid uncertainty relations have been established to set a precision limit for any instruments given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to a quantitative generalization of the Wigner–Araki–Yanase theorem on the precision limit of measurements under conservation laws. Applying this, a rigorous lower bound is obtained for the gate error probability of physical implementations of Hadamard gates on a standard qubit of a spin 1/2 system by interactions with control fields or ancilla systems obeying the angular momentum conservation law.
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.