2000/10/31 by Stephen D. Bartlett, S. D. Bartlett, Dien A. Rice +7 · 1 citation
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Radioactive Decay and Measurement Techniques #quant-ph
paper · pdf · doi:10.1103/physreva.63.042310
published as Phys. Rev. A 63, 042310 (2001) · 3 figures
arxiv created 2001/03/21 · openalex publication_date 2001/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.