General Theory of Overmeasurement of Discrete Quantum Observables and Application to Simultaneous Measurement

TL;DR

This paper develops a comprehensive theory of overmeasurement for discrete quantum observables, including refinements and coarsenings, and applies it to analyze the set of all possible simultaneous measurements of compatible observables.

Contribution

It introduces a complete framework for overmeasurement, extending the understanding of measurement refinements and their application to simultaneous measurement in quantum mechanics.

Findings

Determines the set of all simultaneous measurements for compatible observables.

Provides a broad theoretical foundation for overmeasurement in quantum systems.

Extends the applicability of measurement theory to a wider class of functions of observables.

Abstract

A complete theory of overmeasurement by measuring refinements of observables is presented. It encompasses a wider set of functions of observ- ables (coarsenings) . Thus the theory has a broad potential application.It is applied to a thorough investigation of simultaneous measurements. In partic- ular, the set of all simultaneous measurements for a given pair of compatible observables is determined.