Demystification of quantum entanglement

TL;DR

This paper demonstrates that quantum entanglement and averages can be represented within a classical probabilistic framework using random fields, bridging classical and quantum descriptions.

Contribution

It establishes a rigorous correspondence between classical and quantum probabilistic models for composite systems, including entangled states.

Findings

Quantum averages can be represented as classical averages over random fields.

Quantum mechanics can be viewed as classical statistical mechanics in infinite-dimensional phase space.

The mathematical framework is rigorous, though physical interpretation remains complex.

Abstract

One of the crucial differences between mathematical models of classical and quantum mechanics is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical random fields. It is essentially what Albert Einstein was dreamed of. Quantum mechanics is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem (which will not be discussed in this paper).