Thomas rotation and the mixed state geometric phase

摘要: It is shown that Uhlmann's parallel transport of purifications along a path mixed states represented by 2 × density matrices just the path-ordered product Thomas rotations. These rotations are invariant under hyperbolic translations inside Bloch sphere can be regarded as Poincare ball model geometry. A general expression for state geometric phase an arbitrary geodesic triangle in terms Bures fidelities derived. The formula gives back solid angle result well known from studies pure phase. also this anholonomy reinterpreted non-Abelian entangled living suitable restriction quaternionic Hopf bundle. In picture Pancharatnam spinors.