The linear and nonlinear propagation characteristics of low-frequency obliquely propagating magnetoacoustic waves in dense electron–positron–ion magnetoplasmas are studied in this paper by using the quantum magnetohydrodynamic (QMHD) model. A quantum Kadomtsev–Petviashvili (KP) equation is derived by using the reductive perturbation technique. The dependence of the fast and slow magnetoacoustic solitary waves on the positron concentration, the obliqueness parameter θ and the magnetic field is also investigated. The present investigation may have relevance to dense astrophysical environments where the quantum effects are expected to dominate.