Li Gao, University of Houston
Fisher information is a measure of the amount of information that an observable random variable X carries about an unknown parameter theta. One important application of classical Fisher information is sufficient statistic: a statistic T=T(X) is sufficient for X_theta if and only if the Fisher information is preserved by T. In this talk, I talk about quantum Fisher information (QFI) and its relation to the sufficiency as recoverability via a quantum channel. It turns out that the quantum sufficiency are not guaranteed by the preservation of SLD or RLD Fisher Information, which are the two most considered QFIs in the literature. Nevertheless, the sufficiency is equivalent to the preservation of a large family of “regular” QFIs, just as the classical case. This is a joint work with Iman Marvian, Haojian Li and Cambyse Rouze.