极大似然，最小努力
Maximum Likelihood, Minimum Effort
摘要：
给出了一种计算高斯噪声下的极大似然混合量子态（密度矩阵为$ρ$）的有效方法.我们的方法的工作原理是首先改变基产生一个候选的密度矩阵$μ$，它可能有非物理（负）的本征值，然后找到最近的物理状态下的2-范数。我们的算法在最坏的情况下采用$O(d^4)$作为基变化加上$O(d^3)$用于寻找$ρ$，其中$d$是量子态的维数。在测量基是泡利算子串的特殊情况下，基的改变也只需要$O(d^3)$。该算法的主力是一种新的线性时间方法，用于找到最接近的概率分布（在欧几里德距离）的一组实数和1。
英文摘要：
We provide an efficient method for computing the maximum likelihood mixed quantum state (with density matrix $ρ$) given a set of measurement outcome in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix $μ$ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst $O(d^4)$ for the basis change plus $O(d^3)$ for finding $ρ$ where $d$ is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only $O(d^3)$ as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one.
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