Correlation induced non-Abelian quantum holonomies

TL;DR

This paper introduces a framework for non-Abelian quantum holonomies induced by correlations in two-particle interferometry, revealing how correlation affects the holonomy group and encompassing the Lévay geometric phase for specific systems.

Contribution

It develops a correlation-dependent parallel transport condition leading to non-Abelian holonomies, extending the understanding of geometric phases in quantum systems.

Findings

Holonomy group is generally non-Abelian with correlations

Holonomy becomes Abelian for uncorrelated systems

Framework includes Lévay geometric phase for two-qubit systems

Abstract

In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the L\'{e}vay geometric phase [2004 {\it J. Phys. A: Math. Gen.} {\bf 37} 1821] in the case of two-qubit systems undergoing local SU(2) evolutions.