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Schrodinger Encounters Fisher and Rao: A Survey

Léonard Monsaingeon,Dmitry Vorotnikov

GEOMETRIC SCIENCE OF INFORMATION (GSI 2021)（2021）

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Abstract
In this short note we review the dynamical Schrodinger 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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Key words
Schrodinger problem, Fisher-Rao space, Optimal transport, Fisher information, Entropy
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