Unitary transformations for testing Bell inequalities

S. D. Bartlett, D. A. Rice, B. C. Sanders, J. Daboul, H. De Guise

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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 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.

Original languageEnglish
Article number042310
Pages (from-to)1-10
Number of pages10
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number4
StatePublished - 1 Jan 2001

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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