Schr\"odinger encounters Fisher and Rao: a survey
L\'eonard Monsaingeon, Dmitry Vorotnikov
TL;DR
This paper surveys the Schr"odinger problem within the non-commutative Fisher-Rao space, exploring its connections to Gaussian optimal transport, entropy, and quantum Fisher information, providing a comprehensive overview of this mathematical framework.
Contribution
It offers a self-contained review of the Schr"odinger problem in the non-commutative Fisher-Rao space, highlighting its links to various quantum and classical information measures.
Findings
Connections between Schr"odinger problem and Gaussian optimal transport
Insights into entropy and quantum Fisher information in this context
Clarification of the mathematical structure of non-commutative Fisher-Rao space
Abstract
In this short note we review the dynamical Schr\"odinger problem on the non-commutative Fisher-Rao space of positive semi-definite matrix-valued measures. The presentation is meant to be self-contained, and we discuss in particular connections with Gaussian optimal transport, entropy, and quantum Fisher information.
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