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It is shown that optical experimental tests of Bell inequality violations canbe described by SU(1,1) transformations of the vacuum state, followed by photoncoincidence detections. The set of all possible tests are described by variousSU(1,1) subgroups of Sp(8,$\Bbb R$). In addition to establishing a commonformalism for physically distinct Bell inequality tests, the similarities anddifferences of post--selected tests of Bell inequality violations are also madeclear. A consequence of this analysis is that Bell inequality tests areperformed on a very general version of SU(1,1) coherent states, and thetheoretical violation of the Bell inequality by coincidence detection iscalculated and discussed. This group theoretical approach to Bell states isrelevant to Bell state measurements, which are performed, for example, inquantum teleportation.Comment: 3 figure

Unitary transformations for testing Bell inequalities