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Three-qubit topological phase on entangled photon pairs

We propose an experiment to observe the topological phases associated with cyclic evolutions, generated by local SU(2) operations, on three-qubit entangled states prepared on different degrees of freedom of entangled photon pairs. The topological phases reveal the nontrivial topological structure of the local SU(2) orbits. We describe how to prepare states showing different topological phases, and discuss their relation to entanglement. In particular, the presence of a $π/2$ phase shift is a signature of genuine tripartite entanglement in the sense that it does not exist for two-qubit systems.