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Related Experiment Video

Updated: Jul 8, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Published on: May 30, 2014

Wigner-Araki-Yanase Theorem for Continuous and Unbounded Conserved Observables.

Yui Kuramochi¹, Hiroyasu Tajima^2,3

¹Department of Physics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0385, Japan.

Physical Review Letters

|December 10, 2023

Summary

The Wigner-Araki-Yanase (WAY) theorem is extended to unbounded observables. This proves the impossibility of exact position measurements under momentum conservation, impacting quantum measurement theory.

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Area of Science:

Quantum Mechanics
Mathematical Physics

Background:

The Wigner-Araki-Yanase (WAY) theorem connects conservation laws with measurement commutativity.
Existing proofs are limited to bounded or discrete observables, excluding continuous ones like momentum.

Purpose of the Study:

To generalize the WAY theorem for unbounded and continuous conserved observables.
To investigate the implications for exact quantum measurements and unitary channel implementations.

Main Methods:

Extension of the WAY theorem under the Yanase condition for unbounded observables.
Analysis of projective measurements and unitary channel implementations in quantum systems.

Main Results:

The generalized WAY theorem is established for continuous observables.
Exact projective position measurements under momentum conservation are shown to be impossible.
Unitary channel implementations under conservation laws depend on the spectrum of the conserved observable.

Conclusions:

The study provides a more comprehensive understanding of the WAY theorem's applicability.
It demonstrates fundamental limitations in performing certain quantum measurements exactly.
Findings have implications for quantum information processing and experimental quantum mechanics.