Characterization of Entanglement via Non-Existence of a Subquantum Random Field

Abstract

Any pure state $|\Psi ⟩$ of a compound system $S=(S_1,S_2)$ with the state space $H=H_1\otimes H_2$ determines a kind of covariance operator ${\hat{D}}_{\Psi }$ acting in the Cartesian product $H=H_1\times H_2$. If this operator is positively defined, then it determines a random field valued in $H$. In this case compound quantum system $S$ can be treated as a classical random field system whose configuration space is not tensor, but Cartesian product space. It happens that ${\hat{D}}_{\Psi }\ge 0$ and a subquantum process exists if and only if quantum state $|\Psi ⟩$ is not entangled. The technical framework used in this note is already presented by von Neumann.