Fractional topological phase for entangled qudits

TL;DR

This paper explores the topological properties of entangled qudits, revealing a fractional topological phase during cyclic evolutions, with geometric phases linked to entanglement measures.

Contribution

It introduces the concept of fractional topological phases in entangled qudits and analyzes their geometric and topological features during unitary evolutions.

Findings

Identification of different evolution sectors in entangled qudits

Explicit calculation of geometric phase in terms of concurrence

Prediction of fractional topological phases for maximally entangled states

Abstract

We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their geometrical and topological aspects are analyzed. The geometric phase is explicitly calculated in terms of the concurrence. As a main result, we predict a fractional topological phase for cyclic evolutions in the multiply connected space of maximally entangled states.