Reliability of the beam-splitter–based Bell-state measurement

A linear 50-50 beam splitter, together with a coincidence measurement, has been widely used in quantum optical experiments, such as teleportation, dense coding, etc., for interferometrically distinguishing, measuring, or projecting onto one of the four two-photon polarization Bell states |ψ^(-)〉. In this paper, we demonstrate that the coincidence measurement at the output of a beam splitter cannot be used as an absolute identifier of the input state |ψ^(-)〉 nor as an indication that the input photons have been projected to the |ψ^(-)〉 state.