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

Physica Scripta

A classical field theory comeback? The classical field viewpoint on triparticle entanglement

Andrei Yu. Khrennikov

Published Feb 1, 2011• 6 citations
Publisher

Abstract

We present the fundamentals of a prequantum model with hidden variables of classical field type—prequantum classical statistical field theory (PCSFT). In some sense, this is the comeback of classical field theory, but with an extension to massive particles. All quantum averages (including correlations of entangled systems) can be represented as classical field averages and correlations. In the literature, entanglement of biparticle systems (in particular, biphotons) has been represented in the PCSFT framework. In this paper, we consider triparticle entanglement. It is well known that in conventional quantum mechanics, the cases of biparticle and triparticle entanglement are quite different. Roughly speaking, triparticle entanglement is not reducible to biparticle entanglement. The PCSFT approach to entanglement (as a correlation of classical signals) reflects this quantum situation. The PCSFT representations of correlations in biparticle and triparticle systems differ essentially. In particular, from the mathematical viewpoint the latter is fundamentally more complicated than the former.

DOI
10.1088/0031-8949/2011/t143/014013

Related papers

Prequantum Classical Statistical Field Theory: Fundamentals

Andrei Yu. Khrennikov, Andrei Yu. Khrennikov, Gregg S. Jaeger +2 more

We present fundamentals of a prequantum model with hidden variables of the classical field type. In some sense this is the comeback of classical wave mechanics. Our approach also can be considered as incorporation of quantum mechanics into classical signal theory. All quantum averages (including correlations of entangled systems) can be represented as classical signal averages and correlations.

AIP conference proceedings•Jan 1, 2011•2 citations

Prequantum Classical Statistical Field Theory: Fundamentals

Andrei Yu. Khrennikov

We present fundamentals of a prequantum model with hidden variables of the classical field type. In some sense this is the comeback of classical wave mechanics. Our approach also can be considered as incorporation of quantum mechanics into classical signal theory. All quantum averages (including correlations of entangled systems) can be represented as classical signal averages and correlations.

AIP conference proceedings•Jan 1, 2011•2 citations

Correlations of components of prequantum field corresponding to biparticle quantum system

Andrei Yu. Khrennikov

In a series of previous papers we developed a purely wave model of microphenomena, the so-called prequantum classical statistical field theory (PCSFT). Important probabilistic predictions of QM including correlations of entangled systems can be reproduced by PCSFT. In this note we show that our model provides even a possibility to go beyond QM. By PCSFT each conventional QM-observable is represented by the corresponding quadratic functional of the prequantum field. Consideration of nonquadratic functionals in the PCSFT framework extends essentially the class of observables on microsystems, comparing with QM. In this note we restrict our studies to simplest functionals of such type, namely, to the linear functionals. In particular, components of the prequantum field are represented as these functionals. We find their correlations. As an example, we find the correlation between polarization vectors of a pair of entangled photons in the Bell state. This is a new prediction that in principle can be experimentally checked, even if actual experiments may require essential improvements of our present instrumentation.

Europhysics Letters (EPL)•May 1, 2010•27 citations

Classical signal viewpoint to bunching and anti-bunching

Andrei Yu. Khrennikov

The similarity between classical wave mechanics and quantum mechanics (QM) played an important role in the development of QM (starting with works of De Broglie, Schrödinger, "late Einstein", Lamb, Lande, Mandel, Marshall, Santos, Boyer, and many others). We present a new wave-type approach, so called prequantum classical statistical field theory (PCSFT). PCSFT explores an analogy between some quantum phenomena and classical theory of random fields. Quantum systems are interpreted as symbolic representations of such fields (not only for photons, cf. Lande and Lamb, but even for massive particles). All quantum averages and correlations (including composite systems in entangled states) can be represented as averages and correlations for classical random fields. In this paper PCSFT is used to provide a classical signal representation of bunching and anti-bunching. At least the latter is typically considered as essentially quantum (nonclassical) phenomenon.

arXiv:1105.4268•May 21, 2011•1 citation

Correlations of Entangled Systems from Fluctuations of the Prequantum Field: the Case of an Arbitrary Density Operator

Andrei Yu. Khrennikov, Andrei Yu. Khrennikov

Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie’s “double solution” approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson’s stochastic QM and its generalization by Davidson, ‘t Hooft’s models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrödinger. There is no quantum particles at all, only waves. In particular, photons are simply wave‐pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special “prequantum fields”: the electron field, the neutron field and so on. PCSFT claims that (soon or later) people will be able to measure components of these fields: components of the “photonic field” (the classical electromagnetic field of low intensity), electronic field, neutronic field and so on. However, at the moment (in this paper) we restrict our efforts to reproduce “simply” predictions of QM in the classical field framework. We will show that correlations of entangled systems can be obtained from fluctuations of the prequantum field. We consider the most general case: in QM the state is given by the density operator.

AIP conference proceedings•Jan 1, 2010•1 citation

Interplay between theories of quantum and classical signals: classical representation of entanglement

Andrei Yu. Khrennikov

The idea that quantum mechanics (QM) is simply a version of classical field theory is very old. Recently this idea has been realized in a new mathematical framework - on the basis of theory of random fields (L2-valued random variables). Surprisingly (for at least orthodox Copenhagenist) fundamental predictions of QM can be reproduced on the basis of a purely wave model (prequantum classical statistical field theory, PCSFT). In particular, all quantum correlations (including correlations of composite systems in entangled states) can be represented as correlations of classical random signals. These signals fluctuate at the space-time scale which is essentially finer than the scale of quantum measurements. At the moment we are not able to monitor such signals. However, one can expect that increasing of the precision of measurements will provide such a possibility. In this paper we show that bosonic and fermionic correlations can be obtained in the classical field framework. Finally, we stress that QM can be reduced to theory of classical random fields only in the presence of a relatively strong background field.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 8, 2011•0 citations
We present the fundamentals of a prequantum model with hidden variables of classical field type—prequantum classical statistical field theory (PCSFT). In some sense, this is the comeback of classical field theory, but with an extension to massive particles. All quantum averages (including correlations of entangled systems) can be represented as classical field averages and correlations. In the literature, entanglement of biparticle systems (in particular, biphotons) has been represented in the PCSFT framework. In this paper, we consider triparticle entanglement. It is well known that in conventional quantum mechanics, the cases of biparticle and triparticle entanglement are quite different. Roughly speaking, triparticle entanglement is not reducible to biparticle entanglement. The PCSFT approach to entanglement (as a correlation of classical signals) reflects this quantum situation. The PCSFT representations of correlations in biparticle and triparticle systems differ essentially. In particular, from the mathematical viewpoint the latter is fundamentally more complicated than the former.
In a series of previous papers we developed a purely wave model of microphenomena, the so-called prequantum classical statistical field theory (PCSFT). Important probabilistic predictions of QM including correlations of entangled systems can be reproduced by PCSFT. In this note we show that our model provides even a possibility to go beyond QM. By PCSFT each conventional QM-observable is represented by the corresponding quadratic functional of the prequantum field. Consideration of nonquadratic functionals in the PCSFT framework extends essentially the class of observables on microsystems, comparing with QM. In this note we restrict our studies to simplest functionals of such type, namely, to the linear functionals. In particular, components of the prequantum field are represented as these functionals. We find their correlations. As an example, we find the correlation between polarization vectors of a pair of entangled photons in the Bell state. This is a new prediction that in principle can be experimentally checked, even if actual experiments may require essential improvements of our present instrumentation.
The similarity between classical wave mechanics and quantum mechanics (QM) played an important role in the development of QM (starting with works of De Broglie, Schrödinger, "late Einstein", Lamb, Lande, Mandel, Marshall, Santos, Boyer, and many others). We present a new wave-type approach, so called prequantum classical statistical field theory (PCSFT). PCSFT explores an analogy between some quantum phenomena and classical theory of random fields. Quantum systems are interpreted as symbolic representations of such fields (not only for photons, cf. Lande and Lamb, but even for massive particles). All quantum averages and correlations (including composite systems in entangled states) can be represented as averages and correlations for classical random fields. In this paper PCSFT is used to provide a classical signal representation of bunching and anti-bunching. At least the latter is typically considered as essentially quantum (nonclassical) phenomenon.
Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie’s “double solution” approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson’s stochastic QM and its generalization by Davidson, ‘t Hooft’s models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrödinger. There is no quantum particles at all, only waves. In particular, photons are simply wave‐pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special “prequantum fields”: the electron field, the neutron field and so on. PCSFT claims that (soon or later) people will be able to measure components of these fields: components of the “photonic field” (the classical electromagnetic field of low intensity), electronic field, neutronic field and so on. However, at the moment (in this paper) we restrict our efforts to reproduce “simply” predictions of QM in the classical field framework. We will show that correlations of entangled systems can be obtained from fluctuations of the prequantum field. We consider the most general case: in QM the state is given by the density operator.
The idea that quantum mechanics (QM) is simply a version of classical field theory is very old. Recently this idea has been realized in a new mathematical framework - on the basis of theory of random fields (L2-valued random variables). Surprisingly (for at least orthodox Copenhagenist) fundamental predictions of QM can be reproduced on the basis of a purely wave model (prequantum classical statistical field theory, PCSFT). In particular, all quantum correlations (including correlations of composite systems in entangled states) can be represented as correlations of classical random signals. These signals fluctuate at the space-time scale which is essentially finer than the scale of quantum measurements. At the moment we are not able to monitor such signals. However, one can expect that increasing of the precision of measurements will provide such a possibility. In this paper we show that bosonic and fermionic correlations can be obtained in the classical field framework. Finally, we stress that QM can be reduced to theory of classical random fields only in the presence of a relatively strong background field.