Relation between geometric phases of entangled bipartite systems and their subsystems

Abstract

Geometric phases of entangled states of bipartite systems under bilocal unitary evolution and of the mixed states of their subsystems were discussed. It was found that the cyclic geometric phase for entangled states with nondegenerate eigenvalues under bilocal unitary evolution can always be decomposed into a sum of weighted non-modular pure state phases. The results showed that the mixed state geometric phase of one subsystem is generally different from that of the entangled state even if the other subsystem is kept fixed.