Quantum Measurements Constrained by Symmetries

TL;DR

This paper revisits the Wigner-Araki-Yanase theorem, strengthening it by identifying a new relevant condition and extending it to continuous variables like position and momentum.

Contribution

It introduces a previously unrecognized condition affecting quantum measurement limitations and extends the theorem to continuous variables.

Findings

Identified a new condition influencing measurement repeatability.

Extended the theorem to continuous variables such as position and momentum.

Clarified the role of conservation laws in quantum measurement constraints.

Abstract

We revisit the theorem of Wigner, Araki and Yanase (WAY) describing limitations to repeatable quantum measurements that arise from the presence of conservation laws. We will review a strengthening of this theorem by exhibiting and discussing a condition that has hitherto not been identified as a relevant factor. We will also show that an extension of the theorem to continuous variables such as position and momentum can be obtained if the degree of repeatability is suitably quantified.