A General Setting for Geometric Phase of Mixed States Under an Arbitrary Nonunitary Evolution

Abstract

The problem of geometric phase for an open quantum system is reinvestigated in a unifying approach. Two of existing methods to define geometric phase, one by Uhlmann's approach and the other by kinematic approach, which have been considered to be distinct, are shown to be related in this framework. The method is based upon purification of a density matrix by its uniform decomposition and a generalization of the parallel transport condition obtained from this decomposition. It is shown that the generalized parallel transport condition can be satisfied when Uhlmann's condition holds. However, it does not mean that all solutions of the generalized parallel transport condition are compatible with those of Uhlmann's one. It is also shown how to recover the earlier known definitions of geometric phase as well as how to generalize them when degeneracy exists and varies in time.

4 pages, extended results

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• Quantum Metrology: Extended Convexity of Quantum Fisher Information
• Geometric phase in open systems: beyond the Markov approximation and weak coupling limit
• Environmentally-induced effects on a bipartite two-level system: geometric phase and entanglement properties
• Temperature effects on mixed state geometric phase
• Spin bath interactions effects on the geometric phase
• Operational approach to the Uhlmann holonomy
• Decoherence-induced geometric phase in a multilevel atomic system
• Symmetric logarithmic derivative for general n-level systems and the quantum Fisher information tensor for three-level systems
• Quantum renormalization group approach to geometric phases in spin chains
• Uhlmann phase of coherent states and the Uhlmann-Berry correspondence
• A general treatment of geometric phases and dynamical invariants
• Manifestations of quantum holonomy in interferometry
• Separable states and the geometric phases of an interacting two-spin system
• Entanglement-induced geometric phase of quantum states
• Boundary-induced effect encoded in the corrections to the geometric phase acquired by a bipartite two-level system
• A Symmetry Approach to Geometric Phase for Quantum Ensembles
• Geometric Phase in Quantum Synchronization
• Interferometric and Uhlmann phases of mixed polarization states
• Proxy ensemble geometric phase and proxy index of time-reversal invariant topological insulators at finite temperatures
• Fidelity-based supervised and unsupervised learning for binary classification of quantum states
• Non-Abelian quantum holonomy of hydrogen-like atoms
• Witnessing entanglement via the geometric phase in a impurity-doped Bose-Einstein condensate