Extremely strong magnetic fields change the vacuum index of refraction. Although this polarization-dependent effect is small for typical neutron stars, it is large enough to decouple the polarization states of photons travelling within the field. The photon states evolve adiabatically and follow the changing magnetic field direction. The combination of a rotating magnetosphere and a frequency-dependent-state decoupling predicts polarization phase lags between different wavebands, if the emission process takes place well within the light cylinder. This QED effect may allow observations to distinguish between different pulsar-emission mechanisms and to reconstruct the structure of the magnetosphere.