Bures Geometry of the Three-Level Quantum Systems. I

Abstract

We compute, using a formula of Dittmann, the Bures metric tensor (g) for the eight-dimensional convex set of three-level quantum systems, employing a newly-developed Euler angle-based parameterization of the 3 x 3 density matrices. Most of the individual metric elements (g_{ij}) are found to be expressible in relatively compact form, many of them in fact being exactly zero.