Approximate Wigner Approach to Coulomb Entanglement

TL;DR

This paper introduces two new approximations to the two-electron Wigner equation to make modeling Coulomb entanglement computationally feasible, providing insights into entanglement evolution beyond pure states.

Contribution

It proposes a BBGKY-based reduction and a field approximation of the Coulomb-Wigner operator, offering novel methods to study Coulomb entanglement in complex scenarios.

Findings

The field approximation aligns with the orthodox definition of entanglement.

Both models offer different conceptual perspectives on entanglement.

The analysis provides an intuitive physical picture of Coulomb entanglement evolution.

Abstract

The electric interaction between two nearby evolving electrons triggers the correlation between their waves and governs the operation of logical devices called Coulomb entanglers. Of technological interest in the presence of magnetic fields are multi-spatial evolution scenarios beyond pure state descriptions. The two-electron density matrix becomes eight-dimensional even for two-dimensional spatial cases and is thus computationally prohibitive. In this work, we present two new approximations of the two-electron Wigner equation that aim at computational feasibility: a BBGKY approach for reducing the number of variables and a field approximation of the Coulomb-Wigner operator. They exhibit different conceptual aspects that illustrate alternative viewpoints to entanglement: Only the evolution provided by the latter model satisfies the orthodox definition of entanglement. Our analysis, based on the Fredholm integral representation of the models, allows us to develop an intuitive picture and physical insight into the process.