Quark pair angular correlations in the proton: entropy versus entanglement negativity

Abstract

Two-particle correlations in the proton on the light-front are described by a mixed density matrix obtained by tracing over all other, unobserved, degrees of freedom. We quantify genuinely quantum quark azimuthal correlations in terms of the entanglement negativity measure of Quantum Information Theory. While the two-quark state in color space is one of high entropy and weak quantum correlation, we find that a standard three-quark model wave function from the literature predicts an azimuthally correlated state of low entropy and high entanglement negativity. Low entropy is consistent with expectations for many colors (at fixed 't Hooft coupling $g^2 N_c$) but high negativity indicates substantial two-particle quantum correlations at $N_c=3$. Suppressing quantum correlations associated with entanglement negativity strongly modifies quark pair azimuthal moments $\langle \zeta^n \rangle$, $\zeta = \exp(i (\phi_1-\phi_2))$, intrinsic to the proton state. We also describe how to account for the leading ${\cal O}(g^2)$ correction to the density matrix from light-cone perturbation theory which is due to the presence (or exchange) of a gluon in the proton. This correction increases the entropy and reduces the negativity of the density matrix for quark pair azimuthal correlations. Hence, the entanglement negativity measure may provide novel insight into the structure of the proton state of QCD.