Operational approach to the Uhlmann holonomy

Abstract

We suggest a physical interpretation of the Uhlmann amplitude of a density operator. Given this interpretation we propose an operational approach to obtain the Uhlmann condition for parallelity. This allows us to realize parallel transport along a sequence of density operators by an iterative preparation procedure. At the final step the resulting Uhlmann holonomy can be determined via interferometric measurements.

Added material, references, and journal references

References in corpus (19)

• Geometric phases for mixed states in interferometry
• Universal Quantum Estimator
• Direct estimations of linear and non-linear functionals of a quantum state
• Kinematic approach to the mixed state geometric phase in nonunitary evolution
• Generalization of geometric phase to completely positive maps
• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Mixed state geometric phases, entangled systems, and local unitary transformations
• Interference of Quantum Channels
• Phases of quantum states in completely positive non-unitary evolution
• Probability distributions consistent with a mixed state
• Geometric phase for mixed states: a differential geometric approach
• A General Setting for Geometric Phase of Mixed States Under an Arbitrary Nonunitary Evolution
• Uhlmann's geometric phase in presence of isotropic decoherence
• Subspace preserving completely positive maps
• Gluing of completely positive maps
• Subspace local quantum channels
• Operations and single particle interferometry
• Fidelity and Coherence Measures from Interference
• Manifestations of quantum holonomy in interferometry

Cited by in corpus (18)

• Geometry of quantum phase transitions
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Topological indices for open and thermal systems via Uhlmann's phase
• Geometric phases in quantum information
• Observation of topological Uhlmann phases with superconducting qubits
• Transition Probability (Fidelity) and Its Relatives
• Symmetry-protected Topological Phases at Finite Temperature
• The Uhlmann connection in fermionic systems undergoing phase transitions
• Geometric Phases for Mixed States of the Kitaev Chain
• The Holographic Dual of the Entanglement Wedge Symplectic Form
• Islands and Uhlmann phase: Explicit recovery of classical information from evaporating black holes
• A Symmetry Approach to Geometric Phase for Quantum Ensembles
• Geometric Phase in Quantum Synchronization
• Holonomy for Quantum Channels
• Experimentally testable geometric phase of sequences of Everett's relative quantum states
• Non-Abelian quantum holonomy of hydrogen-like atoms
• Parallelity of mixed quantum ensembles