Unitary transformations for testing Bell inequalities

Abstract

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,$\mathbb{R}$). 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.

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References in corpus (5)

• Experimental quantum teleportation
• Violation of Bell inequalities by photons more than 10 km apart
• Entangled SU(2) and SU(1,1) coherent states
• Coherent eavesdropping strategies for the 4-state quantum cryptography protocol
• Proposal for the Measurement of Bell-like Correlations from Continuous Variables

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• Practical Quantum Teleportation of an Unknown Quantum State