  Highly magnetized neutron stars exhibit the vacuum non-linear electrodynamics
effects, which can be well described using the one-loop effective action for
quantum electrodynamics. In this context, we study the propagation and
polarization of pulsar radio emission, based on the post-Maxwellian Lagrangian
from the Heisenberg-Euler-Schwinger action. Given the refractive index obtained
from this Lagrangian, we determine the leading-order corrections to both the
propagation and polarization vectors due to quantum refraction via perturbation
analysis. In addition, the effects on the orthogonality between the propagation
and polarization vectors and the Faraday rotation angle, all due to quantum
refraction are investigated. Furthermore, from the dual refractive index and
the associated polarization modes, we discuss quantum birefringence, with the
optical phenomenology analogous to its classical counterpart.
