Topological phase for entangled two-qubit states

Abstract

We present an unambiguous characterization of the rotation group SO(3) biconnectedness topology using two-qubit maximally entangled states. We show how to generate cyclic evolutions of these states, which are in one-to-one correspondence to closed paths in SO(3). The difference between the well known two classes of such paths translates into the gain of a global phase of $π$ for one class and no phase change for the other. We propose a simple quantum optics interference experiment to demonstrate this topological phase shift.

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