Geometric Phase: a Diagnostic Tool for Entanglement

TL;DR

This paper demonstrates that the non-adiabatic, non-cyclic geometric phase of radiation from a three-level system can serve as a sensitive diagnostic for entanglement and purity in quantum states, with analytical relations to concurrence.

Contribution

It introduces a kinematic approach linking geometric phase to entanglement measures, providing a new diagnostic tool for quantum state analysis.

Findings

Geometric phase relates analytically to concurrence in certain parameter regions.

Rate of change of geometric phase indicates resilience to fluctuations for pure Bell states.

Derivative of geometric phase encodes information on purity and entanglement.

Abstract

Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric phase corresponding to the radiation emitted by a three level cascade system provides a sensitive diagnostic tool for determining the entanglement properties of the two modes of radiation. The nonunitary, noncyclic path in the state space may be realized through the same control parameters which control the purity/mixedness and entanglement. We show analytically that the geometric phase is related to concurrence in certain region of the parameter space. We further show that the rate of change of the geometric phase reveals its resilience to fluctuations only for pure Bell type states. Lastly, the derivative of the geometric phase carries information on both purity/mixedness and entanglement/separability.