Topological phase for entangled two-qubit states

Entangled states play a crucial role in quantum physics, ranging from fundamental aspects to quantum information processing. We show here that entangled two-qubit states can also be used to characterize unambiguously the subtlety of the SO(3) rotation group topology. The well known two distinct families of path in this group are put in one-to-one correspondence with cyclic evolutions of these entangled states, resulting in a pi phase difference. We propose a simple quantum optics interference experiment to demonstrate this topological phase shift.