Information metric, Berry connection and Berezin-Toeplitz quantization for matrix geometry

Understand

We consider the information metric and Berry connection in the context of noncommutative matrix geometry.

• We propose that these objects give a new method of characterizing the fuzzy geometry of matrices.
• We first give formal definitions of these geometric objects and then explicitly calculate them for the well-known matrix configurations of fuzzy $S^2$ and fuzzy $S^4$.
• We find that the information metrics are given by the usual round metrics for both examples, while the Berry connections coincide with the configurations of the Wu-Yang monopole and the Yang monopole for fuzzy $S^2$ and fuzzy $S^4$, respectively.