It is shown that optical experimental tests of Bell inequality violations can 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 $\mathrm{Sp}(8,R).$ In addition to establishing a common formalism for physically distinct Bell inequality tests, the similarities and differences of post-selected tests of Bell inequality violations are also made clear. A consequence of this analysis is that Bell inequality tests are performed on a very general version of SU(1,1) coherent states, and the theoretical violation of the Bell inequality by coincidence detection is calculated and discussed. This group theoretical approach to Bell states is relevant to Bell state measurements, which are performed, for example, in quantum teleportation.It is shown that optical experimental tests of Bell inequality violations can 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 $\mathrm{Sp}(8,R).$ In addition to establishing a common formalism for physically distinct Bell inequality tests, the similarities and differences of post-selected tests of Bell inequality violations are also made clear. A consequence of this analysis is that Bell inequality tests are performed on a very general version of SU(1,1) coherent states, and the theoretical violation of the Bell inequality by coincidence detection is calculated and discussed. This group theoretical approach to Bell states is relevant to Bell state measurements, which are performed, for example, in quantum teleportation.

arXiv:quant-ph/0010049Physical Review AMar 21, 200121 citations

A CHSH Test of Bell's Inequality

Jeremy Karich

Jan 1, 20170 citations

Bell Inequalities

George Jaroszkiewicz

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\mathrm{Sp}(8,R).

In addition to establishing a common formalism for physically distinct Bell inequality tests, the similarities and differences of post-selected tests of Bell inequality violations are also made clear. A consequence of this analysis is that Bell inequality tests are performed on a very general version of SU(1,1) coherent states, and the theoretical violation of the Bell inequality by coincidence detection is calculated and discussed. This group theoretical approach to Bell states is relevant to Bell state measurements, which are performed, for example, in quantum teleportation.