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.

翻译：近期研究已证明所有采样方法均会产生异常值。本文将这一结论扩展至量子信息理论中：大秩投影算子在其像空间中必然包含属于异常态的纯量子态。反之，若投影算子不包含此类异常态，则其必然具有与停机序列的高互信息量，从而呈现特殊性质。因此，诸如舒马赫压缩等使用投影算子的量子编码方案，必然需要借助异常量子态进行通信。