Relation between geometric phases of entangled bipartite systems and their subsystems

This paper focuses on the geometric phase of entangled states of bipartite systems under bilocal unitary evolution. We investigate the relation between the geometric phase of the system and those of the subsystems. It is shown that (1) the geometric phase of cyclic entangled states with nondegenerate eigenvalues can always be decomposed into a sum of weighted nonmodular pure state phases pertaining to the separable components of the Schmidt decomposition, although the same cannot be said in the noncyclic case, and (2) the geometric phase of the mixed state of one subsystem is generally different from that of the entangled state even if the other subsystem is kept fixed, but the two phases are the same when the evolution operator satisfies conditions where each component in the Schmidt decomposition is parallel transported.