Fidelity of Physical Measurements

TL;DR

This paper introduces the concept of fidelity as a universal, prior-independent measure of measurement quality, applicable to both classical and quantum systems, demonstrated through interferometer comparisons.

Contribution

It proposes fidelity based on Shannon mutual information as a new metric for measurement quality, bridging classical and quantum measurement analysis.

Findings

Fidelity provides a prior-independent measure of measurement quality.

Fidelity allows comparison between classical and quantum measurement systems.

Quantum measurements can be quantitatively assessed using the proposed fidelity metric.

Abstract

The fidelity (Shannon mutual information between measurements and physical quantities) is proposed as a quantitative measure of the quality of physical measurements. The fidelity does not depend on the true value of unknown physical quantities (as does the Fisher information) and it allows for the role of prior information in the measurement process. The fidelity is general enough to allow a natural comparison of the quality of classical and quantum measurements. As an example, the fidelity is used to compare the quality of measurements made by a classical and a quantum Mach-Zehnder interferometer.