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

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.

3.5pp, corrected, substantially improved, with new title

References in corpus (4)

• Thermodynamic length in open quantum systems
• Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation
• A simple operational interpretation of the fidelity
• A limit relation for entropy and channel capacity per unit cost