Geometry near rank-changing points on the mixed-state manifold: Bures metric, conical singularities, and Lindblad dynamics (opens in new tab)

We elucidate the Bures metric in quantum state space near a rank-changing point of the density matrix and show contrasting behavior for two-level ($N=2$) systems versus higher-level systems. Due to the smooth pure-state boundary for $N=2$, we prove the apparent metric divergences to be merely coordinate artifacts and present three Lindblad processes exhibiting qualitatively different evolution near rank-changing points, showing geodesic approach...