Operational meaning of the classical fidelity and the path length in Fisher-Kubo-Mori-Bogoliubov geometry

TL;DR

This paper links the minimum entropy production in near-reversible quantum state transport to the Fisher-KMB metric path length, providing an operational interpretation of statistical lengths as measures of residual irreversibility.

Contribution

It establishes a direct relationship between entropy production and Fisher-KMB path length, giving operational meaning to statistical lengths in quantum and classical contexts.

Findings

Minimum entropy production is a simple function of Fisher-KMB path length.

Statistical lengths quantify residual irreversibility in near-reversible transport.

Classical Bhattacharyya fidelity gains operational meaning after eighty years.

Abstract

We show that the minimum entropy production in near-reversible quantum state transport along a path is simple function of the path length measured according to the Fisher-KMB metrics. Hence the sharp values of path lengths, also called statistical lengths, obtain operational meaning to quantify the residual irreversibility in near-reversible state transport. In the classical limit, the Bhattacharyya fidelity obtains a sharp operational meaning after eighty years.