Local Realistic Theory for PDC Experiments Based on the Wigner Formalism

Abstract

In this article we present a local hidden variables model for all experiments involving photon pairs produced in parametric down conversion, based on the Wigner representation o f the radiation field. A modification o f the standard quantum theory of detection is made in order to give a local realistic explanation o f the counting rates in photodetectors. This model involves the existence of a real zeropoint field, such that the vacumm level of radiation lies below the threshold of the detectors.

From Stochastic Optics to the Wigner Formalism: The Role of the Vacuum Field in Optical Quantum Communication Experiments

“…Let us calculate the intensity at the detectors. For simplicity, we consider that only four zeropoint modes enter the crystal, fulfilling the exact matching conditions, so that the operator G (J) can be replaced by 1 (1/2) [19,29]. By putting…”

“…Some reasonable hypotheses concerning the diminishment of the intensity fluctuations, by means of integrations over the surface and the time window of the detectors, could give rise to a possible way to link them by performing a modification of the quantum theory of detection in order to eliminate the "negative probabilities". In [29,30], a local hidden variable model based on a real zeropoint field is presented, along with the conditions for this model to be compatible with the experimental results. Nevertheless, given the constraint imposed by the necessity of a minimum value of the intensity fluctuations [31,32], it prevents a full agreement between these models and the results concerning joint detection experiments.…”

Entanglement and impropriety

“…This approach has been used extensively as a method for classical modeling of certain quantum systems [9]. For example, the relationship to entanglement was studied by deriving a Wigner function representation of spontaneous parametric downconversion through a detailed physical modeling of nonlinear optical processes using a classical zero-point field [10,11].…”

Innsbruck Teleportation Experiment in the Wigner Formalism: A Realistic Description Based on the Role of the Zero-Point Field

“…The Wigner formalism constitutes a complementary approach to the orthodox formulation in the Hilbert space for the study of quantum optical experiments implemented with PDC [17][18][19][20][21][22][23][24][25]. The Wigner function of PDC is positive and allows for an intuitive picture in terms of stochastic processes.…”