Abstract
The notion of operator-valued free Fisher information was introduced. It is a generalization of free Fisher information which was defined by D. Voiculescu on tracial von Neumann algebras. It is proved that the operator-valued free Fisher information is closely related to amalgamated freeness, i. e., the operator-valued free Fisher information of some random variables is additive if and only if these random variables are a free family with amalgamation over a subalgebra. Cramer-Rao inequality in operator-valued settings is also obtained.
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