General Description of Mixed State Geometric Phase
  We consider arbitrary mixed state in unitary evolution and provide a comprehensive description of corresponding geometric phase in which two different points of view prevailing currently can be unified. Introducing an ancillary system and considering the purification of given mixed state, we find that different results of mixed state geometric phase correspond to different choice of the representation of Hilbert space of the ancilla. Moreover we demonstrate that in order to obtain Uhlmann's geometric phase it is not necessary to resort to the unitary evolution of ancilla. 
Mingjun Shi and Jiangfeng Du