Topological phase for entangled two-qubit states and the representation of theSO(3) group

Abstract

We discuss the representation of the SO(3) group by two-qubit maximally entangled states (MES). We analyze the correspondence between SO(3) and the set of two-qubit MES which are experimentally realizable. As a result, we offer a new interpretation of some recently proposed experiments based on MES. Employing the tools of quantum optics we treat in terms of two-qubit MES some classical experiments in neutron interferometry, which showed the π-phase accrued by a spin-1/2 particle precessing in a magnetic field. By so doing, we can analyze the extent to which the recently proposed experiments -and future ones of the same sort -would involve essentially new physical aspects as compared with those performed in the past. We argue that the proposed experiments do extend the possibilities for displaying the double connectedness of SO(3), although for that to be the case it results necessary to map elements of SU (2) onto physical operations acting on two-level systems.

Geometric phases in quantum information

“…[155,156] In the following, we focus on a type of topological phases for entangled systems undergoing local special unitary (SU) evolution; a subclass of SLOCC operations. These topological phases were first discovered for two-qubit systems, [45,[157][158][159] and later generalized to qudit (d-level) pairs [46,160,161] and to multiqubit systems. [47] They may in some cases coincide with the corresponding GPs.…”