On the Uniqueness of the Chentsov Metric in Quantum Information Geometry
M. R. Grasselli, R. F. Streater
TL;DR
This paper proves that in finite-dimensional quantum information geometry, the only monotone metrics with dual (+1) and (-1) affine connections are scalar multiples of the Bogoliubov-Kubo-Mori metric.
Contribution
It establishes the uniqueness of the Bogoliubov-Kubo-Mori metric among monotone metrics with dual affine connections in finite dimensions.
Findings
Uniqueness of the BKM metric proven
Characterization of monotone metrics with dual connections
Clarification of metric properties in quantum information geometry
Abstract
We show that, in finite dimensions, the only monotone metrics for which the (+1) and (-1) affine connections are mutually dual are constant multiples of Bogoliubov-Kubo-Mori metric
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Topics in Algebra · Geometric Analysis and Curvature Flows