Characterisation of an entanglement-free evolution

TL;DR

This paper investigates the conditions under which quantum systems maintain or lose factorisable states during interactions, highlighting that genuine interactions typically induce entanglement unless specific conditions are met.

Contribution

It demonstrates that interacting quantum systems generally cannot preserve factorisable states unless the Hamiltonian does not couple them, and identifies conditions for maintaining factorisability.

Findings

Factorisable states become non-factorisable during interaction unless the Hamiltonian is non-interacting.

Certain conditions allow factorisable states to remain despite mutual interaction.

Analysis of action-at-a-distance interactions in three-dimensional space.

Abstract

Two or more quantum systems are said to be in an entangled or non-factorisable state if their joint (supposedly pure) wave-function is not expressible as a product of individual wave functions but is instead a superposition of product states. It is only when the systems are in a factorisable state that they can be considered to be separated (in the sense of Bell). We show that whenever two quantum systems interact with each other, it is impossible that all factorisable states remain factorisable during the interaction unless the full Hamiltonian does not couple these systems so to say unless they do not really interact. We also present certain conditions under which particular factorisable states remain factorisable although they represent a bipartite system whose components mutually interact and pay a particular attention to the case where the two particles interact mutually through an action at a distance in the three dimensional space.