The Entropic Skin: Spatial Entanglement from the QCD Confinement Boundary

TL;DR

The paper addresses how confinement in QCD imprints entanglement in coordinate space by analyzing the MIT Bag Model. It shows that the bag boundary acts as an entangling gate, yielding a local spin–position entangled state whose surface entropy saturates at $\mathcal{S}_{surf} \approx 0.918$ bits (with $P_\\downarrow(R)=1/3$) and is independent of the bag radius. By deriving the ground-state spinor and the local reduced density matrix, the authors quantify the spin-flip and spin-preservation probabilities and connect interior purity to surface mixing via the boundary condition $i \\gamma^\\mu n_\\mu \\psi = \\psi$. They further discuss the interpretation that this Entropic Skin is a precursor to the pion cloud through an Entanglement Swapping mechanism, offering a coordinate-space picture of the vacuum entanglement observed in high-energy experiments and motivating future studies with Cloudy Bag models. The results provide a concrete link between confinement, chiral dynamics, and coordinate-space entanglement, with potential implications for understanding hadron structure and vacuum correlations.

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, $i γ^μn_μψ= ψ$, 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.

Figures (1)

• Figure 1: The emergence of the "Entropic Skin." The plot shows the local von Neumann entropy of the quark spinor as a function of dimensionless radius $r/R$. The boundary condition acts as an entanglement gate, converting the purity of the interior into a mixed state at the surface. The surface value reaches $\approx 92\%$ of the theoretical maximum for a qubit.