A quantum channel is said to be a mixed-unitary channel if it can be expressed as a convex combination of unitary channels. We prove that, given the Choi representation of a quantum channel, it is NP-hard with respect to polynomial-time Turing reductions to determine whether or not that channel is a mixed-unitary channel. This hardness result holds even under the assumption that the channel is not within an inverse-polynomial distance (in the dimension of the space upon which it acts) of the boundary of the mixed-unitary channels.

中文翻译：

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检测混合幺正量子通道是 NP 难的

如果量子通道可以表示为酉通道的凸组合，则称该量子通道是混合酉通道。我们证明，给定量子通道的 Choi 表示，关于多项式时间图灵约简，确定该通道是否为混合酉通道是 NP 难的。即使假设通道不在混合酉通道边界的逆多项式距离内（在其作用的空间维度上），该硬度结果也成立。