Geometric phases for mixed states in interferometry
  We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that provides a connection-form for obtaining the geometric phase for mixed states. The expression for the geometric phase for mixed state reduces to well known formulas in the pure state case when a system undergoes noncyclic and unitary quantum evolution. 
Erik Sj\"oqvist, Arun K. Pati, Artur Ekert, Jeeva S. Anandan, Marie   Ericsson, Daniel K.L. Oi, and Vlatko Vedral