A Local Hidden Variables Model for Experiments involving Photon Pairs Produced in Parametric Down Conversion

TL;DR

This paper presents a local hidden variables model for photon pair experiments in parametric down conversion, aligning with quantum mechanics under certain conditions and proposing testable constraints that differ from standard quantum theory.

Contribution

It introduces a local hidden variables model based on the Wigner function for photon pair experiments, challenging quantum predictions under specific detection conditions.

Findings

Model agrees with quantum mechanics at low efficiency and high signal levels.

Proposes testable constraints that differ from standard quantum predictions.

Supports the idea that quantum mechanics is compatible with local realism in certain regimes.

Abstract

In previous articles we have developed a theory of down conversion in nonlinear crystals, based on the Wigner representation of the radiation field. Taking advantage of the fact that the Wigner function is always positive in parametric down conversion experiments, we construct a local hidden variables model where the amplitudes of the field modes are taken as random variables whose probability distribution is the Wigner function. In order to achieve our goal we give a model of detection which is fully local but departs from quantum theory. In our model the zeropoint (vacuum) level of radiation lies below a threshold of the detectors and only signals above the threshold are detectable. The predictions of the model agree with those of quantum mechanics if the signal intensities surpase some level and the efficiency is low. This is consistent with the known fact that quantum mechanics is compatible with local realism in that case (a fact called the ``efficiency loophole''). Our model gives a number of constraints which do not follow from the quantum theory of detection and are experimentally testable.