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We apply the Wigner formalism of quantum optics to study the role of thezeropoint field fluctuations in entanglement swapping produced via parametricdown conversion. It is shown that the generation of mode entanglement betweentwo initially non interacting photons is related to the quadruple correlationproperties of the electromagnetic field, through the stochastic properties ofthe vacuum. The relationship between the process of transferring entanglementand the different zeropoint inputs at the nonlinear crystal and the Bell-stateanalyser is emphasized.

Wigner function description of entanglement swapping using parametric down conversion: the role of vacuum fluctuations in teleportation