Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Wigner-PDC description of photon entanglement can still be made completely local

David Rodríguez

Published Nov 16, 2011• 0 citations
OpenAlex

Abstract

Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward subtraction of the average ZPF intensity at the Wigner image of the detection process.

Related papers

Wigner-PDC description of photon entanglement as a local-realistic theory

David Rodríguez

Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward "subtraction" of the average ZPF intensity at the Wigner image of the detection process.

arXiv:1111.3898•Nov 16, 2011•0 citations

Bell tests with photon-entanglement: LHV models and critical efficiencies at the light of Wigner-PDC optics

David Rodríguez

Within the Wigner-PDC picture of photon entanglement, detection "errors" are not independent (though they may look, on average), nor can they be controlled by means of a technological improvement on the detectors. Those two elements make possible the interpretation of experimental evidence without the need to exclude local realism: for that reason, we propose the abandonment of the usual (photon, particle-based) description of (PDC-generated) light states, in favour of an also quantum, but field-theoretical description (QED), a description that finds a one-to-one equivalent in the Wigner-PDC approach we have advocated in recent posts.

arXiv:1112.3531•Dec 15, 2011•0 citations

Wigner-PDC description of photon entanglement as a local theory

David Rodr

from the point of view of the physical behavior of the detectors. To preserve maximum generality, we adopt a non-factorisable expression of joint detection probabilities (we suspect it is a necessary condition to match quantum correlations, an issue we will examine elsewhere): such non-factorability on (the vacuum amplitudes) is simply an indicator of the need to introduce other (vector of) additional variables in the model, that would possibly correspond to other relevant physical variables related to the laser and the state of the crystal. A conjecture: for the simplest possible model, may possibly correspond to the phase of the laser complex amplitude (or its relative value with respect to ’s). As a correction on initial versions or this paper, such additional -dependence is now introduced directly within the intensities Ii( ) ! Ii(; ) at each (the i-th) detector, which introduces no conceptual change in our initial approach but preserves a reasonable dependence of the probability of detection on the incoming intensity alone: Pi(detj; ) f(I(; )) instead of our former Pi(detj; ) f(I( ); ). For completeness, we also treat some closely related issues, such as: (i) the appearance of (detection probability) enhancement in this framework, (ii) the interpretation of that mysterious \subtraction of the average ZPF intensity at the detector, and (iii) why vacuum uctuations are not directly \observable. Points (i) and (iii) are developed in side-notes [14] and [15], respectively. PACS numbers:

•Jan 1, 2012•0 citations

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

Alberto Casado, Trevor W. Marshall, Ramón Risco +1 more

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.

arXiv:quant-ph/0202097•Feb 19, 2002•5 citations

Local Realistic Interpretation of Entangled Photon Pairs in the Weyl-Wigner Formalism

Emilio Santos

A polarization correlation experiment with two maximally entangled photons created by spontaneous parametric down-conversion is studied in the Weyl-Wigner formalism, that reproduces the quantum predictions. A realistic stochastic interpretation is proposed suggesting that an analysis of the experiments more detailed than the Bell approach may be compatible with local realism. Entanglement appears as a correlation between fluctuations of signal and vacuum fields.

arXiv:1908.03924•Frontiers in Physics•Jun 3, 2020•13 citations

Local Realistic Theory for PDC Experiments Based on the Wigner Formalism

Alberto Casado, Ramón Risco-Delgado, Emilio Santos

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 of the radiation field. A modification of the standard quantum theory of detection is made in order to give a local realistic explanation of 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.

arXiv:quant-ph/0103045•Zeitschrift für Naturforschung A•Feb 1, 2001•3 citations
Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward subtraction of the average ZPF intensity at the Wigner image of the detection process.
Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward "subtraction" of the average ZPF intensity at the Wigner image of the detection process.
Within the Wigner-PDC picture of photon entanglement, detection "errors" are not independent (though they may look, on average), nor can they be controlled by means of a technological improvement on the detectors. Those two elements make possible the interpretation of experimental evidence without the need to exclude local realism: for that reason, we propose the abandonment of the usual (photon, particle-based) description of (PDC-generated) light states, in favour of an also quantum, but field-theoretical description (QED), a description that finds a one-to-one equivalent in the Wigner-PDC approach we have advocated in recent posts.
from the point of view of the physical behavior of the detectors. To preserve maximum generality, we adopt a non-factorisable expression of joint detection probabilities (we suspect it is a necessary condition to match quantum correlations, an issue we will examine elsewhere): such non-factorability on (the vacuum amplitudes) is simply an indicator of the need to introduce other (vector of) additional variables in the model, that would possibly correspond to other relevant physical variables related to the laser and the state of the crystal. A conjecture: for the simplest possible model, may possibly correspond to the phase of the laser complex amplitude (or its relative value with respect to ’s). As a correction on initial versions or this paper, such additional -dependence is now introduced directly within the intensities Ii( ) ! Ii(; ) at each (the i-th) detector, which introduces no conceptual change in our initial approach but preserves a reasonable dependence of the probability of detection on the incoming intensity alone: Pi(detj; ) f(I(; )) instead of our former Pi(detj; ) f(I( ); ). For completeness, we also treat some closely related issues, such as: (i) the appearance of (detection probability) enhancement in this framework, (ii) the interpretation of that mysterious \subtraction of the average ZPF intensity at the detector, and (iii) why vacuum uctuations are not directly \observable. Points (i) and (iii) are developed in side-notes [14] and [15], respectively. PACS numbers:
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.
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 of the radiation field. A modification of the standard quantum theory of detection is made in order to give a local realistic explanation of 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.