Dispersive Property of the Quantum Vacuum and the Speed of Light

We want to study the influence of the quantum vacuum on the light propagation. At first, by working in the standard linear quantum theory of the electromagnetic fields, it is shown that the electric permittivity and the magnetic permeability of the vacuum medium are changed; but, the resulting speed of light isn't modified. Then, taking into account nonlinear effects by considering the Euler-Heisenberg Lagrangian, the corresponding zero point (vacuum) energy and the resulting modification of the speed of light are found up to the first non-vanishing correction.