A Symmetry Approach to Geometric Phase for Quantum Ensembles

Abstract

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 Sjöqvist 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)].

17 pages, 7 figures, accepted version

References in corpus (5)

• An experimental observation of geometric phases for mixed states using NMR interferometry
• Measurement of geometric phase for mixed states using single photon interferometry
• Noncyclic Pancharatnam phase for mixed state SU(2) evolution in neutron polarimetry
• Operational approach to the Uhlmann holonomy
• Non-Abelian quantum holonomy of hydrogen-like atoms

Cited by in corpus (5)

• Geometric phases in quantum information
• Margolus-Levitin quantum speed limit for an arbitrary fidelity
• Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states
• Interferometric and Uhlmann phases of mixed polarization states
• Holonomy in Quantum Information Geometry