The Double Covariance Model: A Stochastic Reconstruction of Quantum Entangled States via Interplay of Micro-Macro Time Scales

TL;DR

This paper introduces the Double Covariance Model, a mathematical framework that reconstructs quantum entangled states from classical stochastic processes using a two-scale temporal scheme, bridging micro and macro correlations.

Contribution

The paper presents a novel stochastic model that derives quantum entanglement from classical processes through a dual time-scale approach, offering a new perspective on quantum state reconstruction.

Findings

Reproduces quantum properties using classical stochastic processes.

Demonstrates that quantum correlations can emerge from micro-correlations.

Provides a mathematical framework linking micro and macro time scales in quantum systems.

Abstract

This article presents a concrete mathematical framework for the generation of entangled quantum states from classical stochastic processes. We demonstrate that any density operator $\rho_{AB}$ of a composite system can be derived from the correlations between two underlying stochastic processes, $X(t)$ and $Y(t)$, representing the random fluctuations of its subsystems. This construction utilizes a two-scale temporal scheme - micro and macro time - where quantum correlations emerge as macro-correlations derived from underlying micro-correlations. We propose the Double Covariance Model (DCM), which reproduces the fundamental properties of quantum theory by treating the quantum state as the fourth-order moment structure of an underlying classical probability space.