# Uhlmann phase in composite systems with entanglement

@article{Villavicencio2021UhlmannPI, title={Uhlmann phase in composite systems with entanglement}, author={Jorge Villavicencio and Ernesto Cota and Fernando Rojas and Jes'us A. Maytorena and Daniel Galindo}, journal={Physical Review A}, year={2021} }

We study the geometric Uhlmann phase of entangled mixed states in a composite system made of two coupled spin1 2 particles with a magnetic field acting on one of them. Within a depolarizing channel setup, an exact analytical expression for such a phase in each subsystem is derived. We find an explicit connection to the concurrence of the depolarizing channel density matrix, which allows to characterize the features of the Uhlmann phase in terms of the degree of entanglement in the system. In…

## References

SHOWING 1-10 OF 44 REFERENCES

Observation of topological Uhlmann phases with superconducting qubits

- Physics
- 2016

Topological insulators and superconductors at finite temperature can be characterized by the topological Uhlmann phase. However, a direct experimental measurement of this invariant has remained…

Quantal phase factors accompanying adiabatic changes

- MathematicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1984

A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar…

Geometric phases for mixed states of the Kitaev chain

- Physics, MedicinePhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2016

The intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature is analyzed, and it is argued that it captures quite different physics from that intended.

Measures and applications of quantum correlations

- Mathematics, Physics
- 2016

Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating…

Berry phase in a bipartite system with general subsystem–subsystem couplings

- Physics
- 2007

Abstract The Berry phase in a bipartite system described by the XXZ model is studied in this Letter. We calculate the Berry phase acquired by the bipartite system as well as the geometric phase…

The Geometric Phase in Quantum Systems: Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics

- Physics
- 2003

1. Introduction.- 2. Quantal Phase Factors for Adiabatic Changes.- 3. Spinning Quantum System in an External Magnetic Field.- 4. Quantal Phases for General Cyclic Evolution.- 5. Fiber Bundles and…

Symmetry-protected topological phases at finite temperature

- Physics
- 2015

We have applied the recently developed theory of topological Uhlmann numbers to a representative model of a topological insulator in two dimensions, the Qi-Wu-Zhang model. We have found a stable…

Geometric quantum computation with NMR

- Physics
- 1999

An exciting recent development has been the discovery that the computational power of quantum computers exceeds that of Turing machines [1]. The experimental realisation of the basic constituents of…

A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions

- Physics
- 2016

This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim…

Entangled Systems: New Directions in Quantum Physics

- Mathematics
- 2007

Preface to the English Edition. Preface to the German Edition. 1 The Mathematical Framework. 1.1 Hilbert Vector Space. 1.2 Liouville Operator Space. 1.3 The Elements of Probability Theory. 1.4…