Unitary transformations for testing Bell inequalities - art. no. 042310

It is shown that optical experimental tests of Bell inequality violations c an be described by SU(1,1) transformations of the vacuum state, followed by photon coincidence detections. The set of all possible tests are described by various SU(1,1) subgroups of Sp(8,R). In addition to establishing a com mon formalism for physically distinct Bell inequality tests, the similariti es and differences of post-selected tests of Bell inequality violations an also made clear. A consequence of this analysis is that Bell inequality tes ts are performed on a very general version of SU(1,1) coherent states, and the theoretical violation of the Bell inequality by coincidence detection i s calculated and discussed. This group theoretical approach to Bell states is relevant to Bell state measurements, which are performed, for example, i n quantum teleportation.