  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.
