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Europhysics Letters (EPL)

Entanglement's dynamics from classical stochastic process

Andrei Yu. Khrennikov

Published Nov 1, 2009• 43 citations
Publisher

Abstract

Entanglement is still one of the main mysteries of QM. In this note we show that entanglement and its dynamics can be described by classical (so to say “prequantum”) stochastic processes. This construction supports the original Einstein's attempt to reduce entanglement to correlations induced by the preparation procedure.
DOI
10.1209/0295-5075/88/40005

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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.
Albert Einstein did not believe in completeness of QM. He dreamed of creation of prequantum classical statistical mechanics such that QM will be reproduced as its approximation. He also dreamed of total exclusion of corpuscules from the future model. Reality of Einstein's dream was pure fields' reality. Recently I made his dream come true in the form of so called prequantum classical statistical field theory (PCSFT). In this approach quantum systems are described by classical random fields, e.g., electromagnetic field (instead of photon), electron field or neutron field. In this paper we generalize PCSFT to composite quantum system. It is well known that in QM, unlike classical mechanics, the state of a composite system is described by the tensor product of state spaces for its subsystems. In PCSFT one can still use Cartesian product, but state spaces are spaces of classical fields (not particles). In particular, entanglement is nothing else than correlation of classical random fields, cf. again Einstein. Thus entanglement was finally demystified.