Measurement disturbance and conservation laws in quantum mechanics

TL;DR

This paper explores how measurement errors and disturbances in quantum mechanics are constrained by conservation laws, providing new bounds and generalizations of the WAY theorem, with implications for quantum measurement theory.

Contribution

It introduces novel quantitative bounds linking measurement accuracy, disturbance, and conservation laws, extending the Wigner-Araki-Yanase theorem and analyzing measurement channels' fixed points.

Findings

Derived necessary conditions for non-disturbing measurements

Generalized the Wigner-Araki-Yanase theorem

Characterized the structure of measurement channel fixed points

Abstract

Measurement error and disturbance, in the presence of conservation laws, are analysed in general operational terms. We provide novel quantitative bounds demonstrating necessary conditions under which accurate or non-disturbing measurements can be achieved, highlighting an interesting interplay between incompatibility, unsharpness, and coherence. From here we obtain a substantial generalisation of the Wigner-Araki-Yanase (WAY) theorem. Our findings are further refined through the analysis of the fixed-point set of the measurement channel, some extra structure of which is characterised here for the first time.