Bell's inequalities, multiphoton states and phase space distributions

Abstract

The connection between quantum optical nonclassicality and the violation of Bell's inequalities is explored. Bell type inequalities for the electromagnetic field are formulated for general states of quantised radiation and their violation is connected to other nonclassical properties of the field. This is achieved by considering states with an arbitrary number of photons and carefully identifying the hermitian operators whose expectation values do not admit any local hidden variable description. We relate the violation of these multi-photon inequalities to properties of phase space distribution functions such as the diagonal coherent state distribution function and the Wigner function. Finally, the family of 4-mode states with Gaussian Wigner distributions is analysed, bringing out in this case the connection of violation of Bell type inequalities with the nonclassical property of squeezing.

16-pages in revtex with three ps figure included using epsf

References in corpus (1)

• Generalized coherent states are unique Bell states of quantum systems with Lie group symmetries

Cited by in corpus (8)

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• U(2) invariant squeezing properties of pair coherent states
• Weak measurement-based state estimation of Gaussian states of one-variable quantum systems
• Re-examination of the role of displacement and photon catalysis operation in continuous variable measurement device-independent quantum key distribution
• Noisy dynamics of Gaussian entanglement: a transient bound entangled phase before separability