If one overlaps two particles at a beamsplitter, interference
effects determine the probabilities to find the two particles
incident one each from a and b
either both in one of the two outputs c and d or to
find one in each output.
Only if two photons are in the state
they will leave the beamsplitter into different
output arms. If one puts detectors there, a click in each of them,
i.e. a coincidence, means the projection of the two photons onto the
state .
For the other three Bell states both photons will exit together through
one of the two output arms. Here polarisation analysis can separate
the state from the states
. (This feature of interferometric
Bell-state analysis was used in the experiment demonstrating
Quantum Dense Coding.)
The identification of all 4 Bell-states will be possible if one couples the
two particles by some interaction. This should be soon possible for
various systems (photons,
atoms
or trapped ions)
which will also form the first 2-qubit quantum logic gates.