We propose an iterative algorithm that computes the maximum-likelihood estimate in quantum state tomography. The optimization error of the algorithm converges to zero at an $O ( ( 1 / k ) \log D )$ rate, where $k$ denotes the number of iterations and $D$ denotes the dimension of the quantum state. The per-iteration computational complexity of the algorithm is $O ( D ^ 3 + N D ^2 )$, where $N$ denotes the number of measurement outcomes. The algorithm can be considered as a parameter-free correction of the $R \rho R$ method [A. I. Lvovsky. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. \textit{J. Opt. B: Quantum Semiclass. Opt.} 2004] [G. Molina-Terriza et al. Triggered qutrits for quantum communication protocols. \textit{Phys. Rev. Lett.} 2004.].

翻译：我们提出一个迭代算法,计算量子状态成像估计值的最大值。算法的优化误差以美元(1/k)\log D)=0的汇率趋同为零,美元表示迭代数的数量和美元美元表示量子状态的维度。算法的单地计算复杂性为$O(D 3+N D =2)$,其中美元表示测量结果的数量。算法的优化误差可视为对美元R\rho R$方法的无参数校正 [A.I. Lvovsky. 在同质成像成像成像成像量子成像图中进行最大值重建。\ textit{J. Opt. B: 量子半级的量子计算复杂性。 Opt.} 2004] [G. Molina-Triza et al. Triggered qutrits for 量子通信协议。\ textitit {Phys.Rev. Lett.}2004]。