标题： 随机自伴量子通道的极限谱分布 显示英文标题

标题： Limiting spectral distribution of random self-adjoint quantum channels

摘要： 我们研究了量子通道的极限谱分布，其Kraus算子被采样为满足某些假设的$n\times n$随机厄米特矩阵。 我们证明了当Kraus秩随着n趋于无穷时，相应的量子通道的极限谱分布（适当缩放后）与半圆分布一致。 当Kraus秩固定时，极限谱分布不再是半圆分布。 它对应于一个显式分布，也可以使用自由概率的工具进行描述。 显示英文摘要

摘要： We study the limiting spectral distribution of quantum channels whose Kraus operators are sampled as $n\times n$ random Hermitian matrices satisfying certain assumptions. We show that when the Kraus rank goes to infinity with n, the limiting spectral distribution (suitably rescaled) of the corresponding quantum channel coincides with the semi-circle distribution. When the Kraus rank is fixed, the limiting spectral distribution is no longer the semi-circle distribution. It corresponds to an explicit law, which can also be described using tools from free probability.