Spin-spin entanglement at high energy

Abstract

Spin correlations offer a quantum-information perspective on the partonic final states produced in high-energy scattering. We discuss the spin-density matrix of a heavy quark-antiquark pair in two complementary small-$x$ processes. In coherent diffractive production, color-singlet exchange enforces an unusually strong relation between entanglement and Bell nonlocality: a longitudinal photon creates a maximally entangled pair, whereas for a transverse photon the pair is generically both entangled and Bell nonlocal, with a model-independent point of maximal entanglement. In inclusive back-to-back production, the density matrix factorizes into a hard spin tensor and the unpolarized and linearly polarized Weizsäcker--Williams gluon distributions. The latter generates an azimuthal modulation and can increase the concurrence when the dijet relative momentum and imbalance are approximately orthogonal. Strikingly, in the saturation model considered, nonlinear effects wash out this modulation for $q_\perp\lesssim 3Q_s$, whereas the dilute BFKL limit, in which $G_2/G_0\to1$, yields a maximal modulation independent of the imbalance magnitude. These results connect quantum-information observables with the Pomeron and saturation physics.