Entanglement entropy, entropy production and time evolution in high energy QCD

TL;DR

This paper investigates the time evolution of entanglement entropy in high energy QCD using the Color Glass Condensate framework, focusing on single events and ensembles, revealing different temporal behaviors.

Contribution

It extends previous work by analyzing entropy production in a single event and compares it with ensemble averages within the high energy QCD context.

Findings

Single event entropy shows strong time dependence.

Ensemble entropy exhibits weak time dependence.

Monogamy of entanglement explains the difference in behaviors.

Abstract

Working in the framework of the Color Glass Condensate effective theory of high energy QCD, we revisit the momentum space entanglement entropy of the soft gluons produced in high energy dilute-dense collisions. We extend the work of~\cite{Kovner:2015hga} by considering entropy produced in a single event. This entropy arises due to decoherence of eigenstates with different energies during the time evolution after the collisions with the target. We define it rigorously as the entanglement entropy of the produced system with the experimental apparatus. We compute the time dependent single event entropy in the limit of weak projectile field. Further we compute the entropy for the ensemble of events defined by the McLerran-Venugopalan model for the projectile wave function. Interestingly the entropy of the ensemble has a much weaker time dependence than the entropy in any single event. We attribute this feature to the so called monogamy of entanglement.