  In recent results, it has been proven that all sampling methods produce
outliers. In this paper, we extend these results to quantum information theory.
Projectors of large rank must contain pure quantum states in their images that
are outlying states. Otherwise, the projectors are exotic, in that they have
high mutual information with the halting sequence. Thus quantum coding schemes
that use projections, such as Schumacher compression, must communicate using
outlier quantum states.
