Bell measurements as a witness of a dualism in entanglement

We show how a property of dualism, which can exist in the entanglement of identical particles, can be tested in the usual photonic Bell measurement apparatus with minor modifications. Two different sets of coincidence measurements on the same experimental setup consisting of a Hong-Ou-Mandel interferometer demonstrate how the same two-photon state can emerge entanglement in the polarization or the momentum degree of freedom depending on the dynamical variables used for labeling the particles. Our experiment demonstrates how the same source can be used as both a polarization entangled state, as well as a dichotomic momentum entangled state shared between distant users Alice and Bob in accordance to which sets of detectors they access. When the particles become distinguishable by letting the information about one of the variables to be imprinted in yet another (possibly inaccessible) system or degree of freedom, the feature of dualism is expected to vanish. We verify this feature by polarization decoherence (polarization information in environment) or arrival time difference, which both respectively destroy one of the dual forms of entanglement.