L\"{u}ders Theorem for Unsharp Quantum Measurements

TL;DR

This paper extends L"uders' theorem from sharp to certain unsharp quantum measurements, exploring conditions under which measurements do not disturb other observables and discussing implications for relativistic quantum theory.

Contribution

It generalizes L"uders' theorem to unsharp observables and analyzes the conditions for non-disturbance in quantum measurements.

Findings

Extension of L"uders' theorem to unsharp observables

Conditions for measurement non-disturbance established

Implications for local relativistic quantum theory discussed

Abstract

A theorem of L\"{u}ders states that an ideal measurement of a sharp discrete observable does not alter the statistics of another sharp observable if, and only if, the two observables commute. It will be shown that this statement extends to certain pairs of unsharp observables. Implications for local relativistic quantum theory will be discussed.