Experimental Orthogonalization Of Highly Overlapping Quantum States With Single Photons

We experimentally realize a nonlinear quantum protocol for single-photon qubits with linear optical elements and appropriate measurements. Quantum nonlinearity is induced by postselecting the polarization qubit based on a measurement result obtained for the spatial degree of freedom of the single photon which plays the role of a second qubit. Initially, both qubits are prepared in the same quantum state and an appropriate two-qubit unitary transformation entangles them before the measurement of the spatial part. We analyze the result by quantum state tomography of the polarization degree of freedom. We then demonstrate the usefulness of the protocol for quantum state discrimination by iteratively applying it to either of two slightly different quantum states which rapidly converge to different orthogonal states by the iterative dynamics. Our work creates an opportunity to employ effective quantum nonlinear evolution in quantum information processing.