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 be en an elusive concept in the past. We define the parallel transport conditi on that provides a connection form for obtaining the geometric phase for mi xed states. The expression for the geometric phase for mixed state reduces to well known formulas in the pure state case when a system undergoes noncy clic and unitary quantum evolution.