We study spontaneous parametric down conversion of terahertz photons into entangled plasmon pairs in graphene.This process is permitted by both symmetry and kinematics in a ribbon with an electron density gradient. We show that the conversion rate is maximized in ribbons containing lateral p-n junctions. We discuss how the quantum entanglement of the generated pairs can be measured by near-field optics techniques. We specify requirements for achieving plasmonic two-mode squeezed states and plasmonic instabilities in the presence of losses.We also study nonlinear plasmonic effects in a large-area uniformly doped graphene sheets due to third-order optical response.