A Symmetry Approach to Geometric Phase for Quantum Ensembles

We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann’s standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the ‘interferometric’ geometric phase of Sj"{o}qvist et al. [Phys. Rev. Lett. 85 2845 - 2849 (2000)], and for more generally evolving open systems it gives rise to the generalization of the interferometric geometric phase due to Tong et al. [Phys. Rev. Lett. 93 080405 (2004)].