The Entropic Skin: Spatial Entanglement from the QCD Confinement Boundary

TL;DR

This paper shows that the boundary of the MIT Bag Model creates maximal spatial entanglement for confined quarks, revealing an 'Entropic Skin' that links confinement to quantum entanglement and has implications for chiral symmetry breaking.

Contribution

It introduces the concept of the 'Entropic Skin' as a boundary-induced entanglement mechanism in the MIT Bag Model, connecting confinement with quantum entanglement.

Findings

Surface entropy density is approximately 0.918 bits, close to the qubit limit.

The boundary condition acts as an entangling gate for quark states.

The entropy is independent of the bag radius.

Abstract

Recent investigations into High-Energy QCD have identified entanglement entropy as a crucial observable, linking parton distributions to the structure of the quantum vacuum. While momentum-space entanglement has been extensively studied in Deep Inelastic Scattering (DIS), the spatial realization of this entanglement in confined systems remains an open question. In this Letter, we demonstrate that the confining boundary of the MIT Bag Model acts as an ``Entropic Skin,'' generating maximal Spin-Position entanglement. We calculate the local reduced density matrix for the confined quark and show that the linear boundary condition, $i \gamma^\mu n_\mu \psi = \psi$, acts as an entangling gate. The surface entropy density reaches a geometric invariant of $\approx 0.918$ bits ($92\%$ of the qubit limit), independent of the bag radius. We discuss the implications of this result for Chiral Symmetry breaking and propose that this boundary entropy is the precursor to the pion cloud in effective field theories.