Bures geometry of the three-level quantum systems. II

TL;DR

This paper numerically analyzes the Bures geometry of three-level quantum systems, focusing on curvature integrals to deepen understanding of quantum state space geometry, building upon Dittmann's prior theoretical work.

Contribution

It provides numerical approximations of curvature-related integrals on the Bures manifold for three-level systems, extending previous theoretical insights.

Findings

Numerical estimates of curvature integrals on the Bures manifold.

Insights into the geometric structure of three-level quantum systems.

Connections to Yang-Mills equations in quantum geometry.

Abstract

For the eight-dimensional Riemannian manifold comprised by the three-level quantum systems endowed with the Bures metric, we numerically approximate the integrals over the manifold of several functions of the curvature and of its (anti-)self-dual parts. The motivation for pursuing this research is to elaborate upon the findings of Dittmann in his paper, "Yang-Mills equation and Bures metric" (quant-ph/9806018).