  For a particle travelling through an interferometer, the trade-off between
the available which-way information and the interference visibility provides a
lucid manifestation of the quantum mechanical wave-particle duality. Here we
analyze this relation for a particle possessing an internal degree of freedom
such as spin. We quantify the trade-off with a general inequality that paints
an unexpectedly intricate picture of wave-particle duality when internal states
are involved. Strikingly, in some instances which-way information becomes
erased by introducing classical uncertainty in the internal degree of freedom.
Furthermore, even imperfect interference visibility measured for a suitable set
of spin preparations can be sufficient to infer absence of which-way
information. General results are illustrated with a proof-of-principle single
photon experiment.
