where D B is the Bures distance between the starting and ending states. The Bures distance is geodesic, giving the shortest possible distance of any continuous curve connecting two points, with σ σ H ( t ) understood as an infinitessimal path length along a curve parametrized by t . Equivalently, the time τ τ taken to evolve from ρ ρ to ρ ρ ′ is bounded as