Quantum entanglement correlations in double quark PDFs

TL;DR

The paper addresses whether quantum entanglement exists in double quark PDFs by constructing the full two-quark density matrix from a simple three-quark light-cone wavefunction and applying quantum-information diagnostics (entanglement negativity via partial transpose). It uses the PEN procedure to purge entanglement negativity and examines the impact on the double PDF, showing that quantum correlations can significantly modify the dPDF in asymmetric momentum regions. It extends the analysis to scale evolution by computing a first one-gluon emission correction, demonstrating cancellation of soft divergences and that the diagonal part obeys the standard DGLAP evolution, while the full density matrix includes nontrivial off-diagonal evolution. Preliminary numerical results at higher $Q^2$ indicate that quantum correlations survive and can become most pronounced in nearly symmetric momentum fractions, offering a new handle on parton correlations beyond classical factorization. This work motivates a full resummed evolution and underscores the utility of QIT concepts to reveal non-classical correlations in hadronic structure.

Abstract

Methods from Quantum Information Theory are used to scrutinize quantum correlations encoded in the two-quark density matrix over light-cone momentum fractions $x_1$ and $x_2$. A non-perturbative three quark model light-cone wavefunction predicts significant non-classical correlations associated with the "entanglement negativity" measure for asymmetric and small quark momentum fractions. We perform one step of QCD scale evolution of the entire density matrix, not just its diagonal (dPDF), by computing collinearly divergent corrections due to the emission of a gluon. Finally, we present first qualitative numerical results for single-step scale evolution of quantum entanglement correlations in double quark PDFs. At a higher $Q^2$ scale, the non-classical correlations manifest in the dPDF for nearly symmetric momentum fractions.

Figures (5)

• Figure 1: Eigenvalue spectrum of the partial transpose $\tilde{\rho}^{T_2}$ for $\frac{1}{\Delta\xi} = \frac{1}{\Delta\eta} =$ 20, 40, 80, 160. The red arrows at the origin signify $\delta(\lambda)$ peaks in the continuum limit. We have chosen to show these peaks as arrows labeled with their correct height, rather than plotting these peaks and obscuring the nonzero eigenvalues.
• Figure 2: Left: the double quark PDF of the LC quark model (see text) in the $x_1$-$x_2$ plane. Right: the ratio of the double quark PDF after removal of the entanglement negativity to the original dPDF shown on the left.
• Figure 3: Some selected slices of constant $x_2$ for the ratio of the dPDF to the product of two PDFs. The vertical dashed line represents the kinematic boundary where $x_1+x_2=1$. The dash-dotted and dashed curves correspond to the GS Gaunt:2009re and BA Broniowski:2013xba models given in eqs. (\ref{['eq:GS-dPDF']},\ref{['eq:BA-dPDF']}), respectively. The solid and dotted curves refer to the dPDF obtained here from the Brodsky-Schlumpf model LCwf Schlumpf:1992vqBrodsky:1994fz before and after the removal of quantum correlations via the PEN algorithm.
• Figure 4: Two diagrams representing, respectively, the emission and absorption of a gluon by quark 1, and the exchange of a gluon between quarks 1' and 1. The dashed line represents the insertion of two-quark basis states. There are six diagrams of the first type and three of the second type.
• Figure 5: Contour plots of the dPDF at $Q^2/Q^2_0 = 100$ with $\alpha_s = 0.1$, $x=0.1$, and $Q_0 = m_q$ as a function of $\eta=x_1+x_2$ and $\xi = x_1/(x_1+x_2)$ (top), and $x_1$ and $x_2$ (bottom). Left: the dPDF obtained here from the Brodsky-Schlumpf model LCwf with corrections due to collinear gluon emission. Right: same, after the removal of quantum correlations via the PEN transformation.