Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model

TL;DR

This paper investigates the quantum properties of the hadron wavefunction at small x within the CGC framework, analyzing the reduced density matrix of soft gluons, its non-diagonality, and implications for thermalization and entropy.

Contribution

It introduces a detailed analysis of the reduced density matrix for soft gluons, highlighting its non-diagonality and the concept of ignorance density matrix, along with the thermal basis diagonalization and new quasi-particle states.

Findings

Reduced density matrix is not diagonal in the particle number basis.

Entropy of ignorance exceeds entanglement entropy.

Density matrix can be diagonalized in a thermal basis, indicating thermalization.

Abstract

To study quantum properties of the hadron wavefunction at small x, we derived the reduced density matrix for soft gluons in the CGC framework. We explicitly showed that the reduced density matrix is not diagonal in the particle number basis. The off-diagonal components are usually ignored in the conventional parton model. We thus defined the density matrix of ignorance by keeping only the part of the reduced density matrix which can be probed in a limited set of experimental measurements. We calculated Von Neumann entropy for both the reduced and ignorance density matrices. The entropy of ignorance is always greater than the entanglement entropy (computed drom the reduced density matrix) of gluons. Finally, we showed that the CGC reduced density matrix for soft gluons can be diagonalized in a thermal basis with Boltzmann weights suggesting thermalization of new quasi-particle states which we dubbed entangolons.