Topological phases and multiqubit entanglement
Markus Johansson, Marie Ericsson, Kuldip Singh, Erik Sjöqvist, Mark S. Williamson · Physical Review A · 2012
Global phase factors of topological origin, resulting from cyclic local $\mathit{SU}$ evolution, called topological phases, were first described in [Phys. Rev. Lett. 90, 230403 (2003)], in the case of entangled qubit pairs. In this paper we investigate topological phases in multiqubit systems as the result of cyclic local $\mathit{SU}(2)$ evolution. These phases originate from the topological structure of the local $\mathit{SU}(2)$ 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.