A geometric mean for completely positive maps on von Neumann algebras is constructed via Pusz-Woronowicz forms, shown compatible with Choi matrices in finite dimensions, and used to obtain a unified Lebesgue decomposition.
Uhlmann; Relative entropy and the Wigner--Yanase--Dyson--Lieb concavity in an interpolation theory
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Geometric Means and Lebesgue-type Decomposition of Completely Positive Maps
A geometric mean for completely positive maps on von Neumann algebras is constructed via Pusz-Woronowicz forms, shown compatible with Choi matrices in finite dimensions, and used to obtain a unified Lebesgue decomposition.