Topological phases and multiqubit entanglement

Abstract

Global phase factors of topological origin, resulting from cyclic local SU evolution, called topological phases, were first described in, in the case of entangled qubit pairs. In this paper we investigate topological phases in multiqubit systems as the result of cyclic local SU(2) evolution. These phases originate from the topological structure of the local SU(2) orbits and are an attribute of most entangled multiqubit systems. We discuss the relation between topological phases and stochastic local operations and classical communication (SLOCC)-invariant polynomials and give examples where topological phases appear. A general method to find the values of the topological phases in an n-qubit system is described and a complete list of these phases for up to seven qubits is given. © 2012 American Physical Society.