Simple optical measurement of the overlap and fidelity of quantum states: An experiment

We present the experimental results of measurements of the overlap of both pure and mixed polarization states of photons. The fidelity and purity of mixed states were also measured. The experimental apparatus exploits the fact that a beam splitter can distinguish the singlet Bell state from the other Bell states, i.e., it realizes projections into the symmetric and antisymmetric subspaces of photons' Hilbert space.