  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.
