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.

Eight pages, LaTeX, two postscript figures, minor changes, to appear in J. Geom. Phys

References in corpus (4)

• State estimation for large ensembles
• Bures Measures over the Spaces of Two and Three-Dimensional Density Matrices
• Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
• Exact Bures Probabilities that Two Quantum Bits are Classically Correlated

Cited by in corpus (4)

• Random Bures mixed states and the distribution of their purity
• Transition Probability (Fidelity) and Its Relatives
• An Explicit Computation of the Bures Metric Over the Space of $N$-Dimensional Density Matrices
• Calculation of the unitary part of the Bures measure for N-level quantum systems