Mixed state geometric phases, entangled systems, and local unitary transformations

Abstract

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires uni-local transformations and is therefore essentially a property of the system alone.

minor changes, journal reference added

References in corpus (4)

• Geometric Manipulation of Trapped Ions for Quantum Computation
• Non-adiabatic conditional geometric phase shift with NMR
• On singularities of the mixed state phase
• Reply to `Singularities of the mixed state phase'

Cited by in corpus (48)

• Kinematic approach to the mixed state geometric phase in nonunitary evolution
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Experimental demonstration of the stability of Berry's phase for a spin-1/2 particle
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Density Matrix Topological Insulators
• Topological indices for open and thermal systems via Uhlmann's phase
• Geometric phases in quantum information
• Observation of topological Uhlmann phases with superconducting qubits
• Measurement of geometric phase for mixed states using single photon interferometry
• Weak Values with Decoherence
• Geometric phases of light: insights from fibre bundle theory
• Symmetry-protected Topological Phases at Finite Temperature
• Phase Dynamics of Two Entangled Qubits
• A General Setting for Geometric Phase of Mixed States Under an Arbitrary Nonunitary Evolution
• Observation of nonadditive mixed state phases with polarized neutrons
• Temperature effects on mixed state geometric phase
• Off-diagonal generalization of the mixed state geometric phase
• Geometric phase of a quantum dot system in nonunitary evolution
• Effect of intersubsystem coupling on the geometric phase in a bipartite system
• Observation of Entanglement-Dependent Two-Particle Holonomic Phase
• Gauge freedom in observables and Landsbergs nonadiabatic geometric phase: pumping spectroscopy of interacting open quantum systems
• Geometric Phases for Mixed States of the Kitaev Chain
• Operational approach to the Uhlmann holonomy
• Composite Geometric Phase for Multipartite Entangled States
• Non-Markovian Effects on the Geometric Phase
• Topological characterization of one-dimensional open fermionic systems
• Mixed State Geometric Phase from Thomas Rotations
• Geometric phases for mixed states and decoherence
• Uhlmann phase of coherent states and the Uhlmann-Berry correspondence
• Manifestations of quantum holonomy in interferometry
• Non-Markovian dynamics of mixed-state geometric phase of dissipative qubits
• Separable states and the geometric phases of an interacting two-spin system
• Geometric Phase: a Diagnostic Tool for Entanglement
• Entanglement-induced geometric phase of quantum states
• Open system geometric phase based on system-reservoir joint state evolution
• Hard-Wall and Non-Uniform Lattice Monte Carlo Approaches to One-Dimensional Fermi Gases in a Harmonic Trap
• A Symmetry Approach to Geometric Phase for Quantum Ensembles
• Off-diagonal quantum holonomy along density operators
• Interferometric and Uhlmann phases of mixed polarization states
• Mixed state geometric phase for neutrino oscillations
• Vacuum condensate, geometric phase, Unruh effect and temperature measurement
• Geometry of decomposition dependent evolutions of mixed states
• The Uhlmann Phase Winding in Bose-Einstein Condensates at Finite Temperature
• Geometric phase and multipartite entanglement of Rydberg atom chains
• Precisely resolve energy-time entanglement by dual channel Fabry-Perot interferometry
• Non-Abelian quantum holonomy of hydrogen-like atoms
• Effect of entanglement on geometric phase for multi-qubit states
• Geometric and holonomic quantum computation