Investigation of the Aharonov-Bohm and Aharonov-Casher Topological Phases for Quantum Entangled States in 2+1 Dimensions

TL;DR

This paper explores the relativistic Aharonov-Bohm and Aharonov-Casher effects in 2+1 dimensions, analyzing their impact on entangled spin-1/2 systems and the CHSH inequality.

Contribution

It provides a relativistic treatment of topological phases in 2+1 dimensions and examines their effects on quantum entanglement and Bell inequality violations.

Findings

The AC phase influences the CHSH correlation function.

Relativistic effects are significant in topological phase interactions.

Topological phases affect quantum entanglement in 2+1 dimensions.

Abstract

Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects are treated fully relativistically in 2+1 dimensions. The influences of the relevant geometric and topological phases on an entangled spin-1/2 system are studied. It is shown that for the AC case the correlation function of the Clauser-Horne-Shimony-Holt (CHSH) inequality for certain choices of the spin measurements depends on the AC phase explicitly.