Generalizations of Berry phase and differentiation of purified state and thermal vacuum of mixed states
arXiv:2205.08679 · doi:10.1016/j.physleta.2022.128553
Abstract
Two representations of mixed states by state-vectors, known as purified state and thermal vacuum, have been realized on quantum computers. While the two representations look similar, they differ by a partial transposition in the ancilla space. While ordinary observables cannot discern the two representations, we generalize the Berry phase of pure quantum states to mixed states and construct two geometric phases that can reflect the partial transposition. By generalizing the adiabatic condition, we construct the thermal Berry phase, whose values from the two representations can be different, However, the thermal Berry phase may contain non-geometrical contributions. Alternatively, we generalize the parallel-transport condition to include the system and ancilla and show the dynamical phase is excluded under parallel transport. The geometrical phase accumulated in parallel transport is the generalized Berry phase, which may or may not differentiate a purified state from a thermal vacuum depending on the protocol. The generalizations of the Berry phase to mixed states may be realized and measured on quantum computers via the two representations to reveal the rich physics of finite-temperature quantum systems.
arXiv comment15 pages, 1 figure
References in corpus (30)
- Topological Insulators
- Topological insulators and superconductors
- Quantum Spin Hall Effect in Graphene
- Separability Criterion for Density Matrices
- Topological Insulators in Three Dimensions
- Classification of topological quantum matter with symmetries
- Topological invariants of time-reversal-invariant band structures
- Quantum Spin Hall Effect
- Geometric phases for mixed states in interferometry
- Traversable Wormholes via a Double Trace Deformation
- Kinematic approach to the mixed state geometric phase in nonunitary evolution
- Geometric phase in open systems
- Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond
- Geometric phases for non-degenerate and degenerate mixed states
- Topology of density matrices
- Probing the topology of density matrices
- Generalization of geometric phase to completely positive maps
- How to Build the Thermofield Double State
- Observation of topological Uhlmann phases with superconducting qubits
- Teleportation Through the Wormhole
- On singularities of the mixed state phase
- Phases of quantum states in completely positive non-unitary evolution
- Reply to `Singularities of the mixed state phase'
- Realizing Physical Approximation of the Partial Transpose
- Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
- Finite-temperature topological phase transitions of spin- systems in Uhlmann processes: General formalism and experimental protocols
- Dynamic process and Uhlmann process: Incompatibility and dynamic phase of mixed quantum states
- Experimental Implementation of the Universal Transpose Operation
- Operational geometric phase for mixed quantum states
- Effect of inter-subsystem couplings on the evolution of composite systems
Cited by in corpus (4)
- Geometric phases of mixed quantum states: A comparative study of interferometric and Uhlmann phases
- Uhlmann phase of coherent states and the Uhlmann-Berry correspondence
- Sjqvist quantum geometric tensor of finite-temperature mixed states
- Mixed-state geometric phases of coherent and squeezed spin states