Several techniques of generating random quantum channels, which act on the set of d-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show that they are mathematically equivalent. We discuss under which conditions they give the uniform Lebesgue measure on the convex set of quantum operations and compare their advantages and computational complexity and demonstrate which of them is particularly suitable for numerical investigations. Additional results focus on the spectral gap and other spectral properties of random quantum channels and their invariant states. We compute the mean values of several quantities characterizing a given quantum channel, including its unitarity, the average output purity, and the 2-norm coherence of a channel, averaged over the entire set of the quantum channels with respect to the uniform measure. An ensemble of classical stochastic matrices obtained due to super-decoherence of random quantum stochastic maps is analyzed, and their spectral properties are studied using the Bloch representation of a classical probability vector.

中文翻译：

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生成随机量子通道

产生随机量子通道的几种技术，它们作用于d的集合维量子态，进行了研究。我们提出了三种解决量子通道采样问题的方法，并表明它们在数学上是等效的。我们讨论了在哪些条件下他们对量子运算的凸集给出了统一的 Lebesgue 测度，并比较了它们的优势和计算复杂性，并证明了它们中的哪一个特别适合数值研究。其他结果集中在随机量子通道及其不变状态的光谱间隙和其他光谱特性上。我们计算了表征给定量子通道的几个量的平均值，包括其单一性、平均输出纯度和通道的 2 范数相干性，在整个量子通道集上相对于统一度量取平均值。