Schr\"odinger encounters Fisher and Rao: a survey

Léonard Monsaingeon, Dmitry Vorotnikov

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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