A Quantum Outlier Theorem

Abstract: 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.