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Europhysics Letters (EPL)

Correlations of components of prequantum field corresponding to biparticle quantum system

Andrei Yu. Khrennikov

Published May 1, 2010• 27 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/90/40004

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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.
In a series of previous papers we developed a purely field model of microphenomena, so called prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of QM including correlations for entangled systems, but it also gives a possibility to go beyond quantum mechanics (QM), i.e., to make predictions of phenomena which could be observed at the subquantum level. In this paper we discuss one of such predictions - existence of nonlocal correlations between prequantum random fields corresponding to {\it all} quantum systems. (And by PCSFT quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are "entangled", but in the sense of classical signal theory. On one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology - for Gaussian random fields with covariance operators corresponding to factorizable quantum states).
We developed a purely field model of microphenomena—prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of quantum mechanics (QM) including correlations for entangled systems, but also gives a possibility to go beyond QM, i.e. to make predictions of phenomena that could be observed at the subquantum level. In this paper, we discuss one such prediction—the existence of nonlocal correlations between prequantum random fields corresponding to all quantum systems. (And by PCSFT, quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are 'entangled', but in the sense of classical signal theory. On the one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology—for Gaussian random fields with covariance operators corresponding to factorizable quantum states).
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.
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.
Recently it was shown that the main distinguishing features of quantum mechanics (QM) can be reproduced by a model based on classical random fields, so called prequantum classical statistical field theory (PCSFT). This model provides a possibility to represent averages of quantum observables, including correlations of observables on subsystems of a composite system (e.g., entangled systems), as averages with respect to fluctuations of classical (Gaussian) random fields. In this note we consider some consequences of PCSFT for quantum information theory. They are based on the observation \cite{W} of two authors of this paper that classical Gaussian channels (important in classical signal theory) can be represented as quantum channels. Now we show that quantum channels can be represented as classical linear transformations of classical Gaussian signal