量子态估计

通用克隆机的极大似然估计

Characterising a universal cloning machine by maximum-likelihood estimation

本文将完全正映射估计的一般方法应用于1-to-2泛协变克隆机。该方法是基于极大似然原则，并利用随机输入状态，以及随机投影测量的输出克隆。下坡单纯形算法适用于似然函数的最大化。

量子测量的极大似然估计

Maximum-likelihood estimation of quantum measurement

极大似然估计被应用于未知量子测量的确定。测量装置对许多不同的量子态进行测量，然后通过极大似然原理从收集的数据中推断出控制测量统计的正算子值测量。与基于线性反演的方法相比，我们的方法总是提供物理上合理的结果。本文以Stern-Gerlach装置为例说明了该方法。

量子估计中的极大似然方法

Maximum-likelihood method in quantum estimation

本文评述了量子估计的极大似然方法，并将其应用于自旋和辐射的密度矩阵的重建以及量子光学中几个重要参数的确定。

利用极大似然估计重构密度矩阵对角元素

Reconstruction of diagonal elements of density matrix using maximum likelihood estimation

席勒等人的实验数据，物理修订信函77（1996）2933，或者使用极大似然估计来评估。给定的数据拟合比标准的确定性方法。尽管如此，这些数据同样适用于整个国家。标准的确定性预测近似对应于这些极大似然解的包络。

Preliminary investigation of a new state estimation technique using device-independent maximum likelihood estimation

In quantum state tomography, the estimated frequencies do not correspond directly to a physical quantum state, due to statistical fluctuations. Thus, one resorts to point estimators that return the state that matches observations the best, and a variety of estimators have been proposed -- linear inversion, least squares, maximum likelihood (ML) -- each making different trade-offs. In this short note, we investigate an alternative approach inspired by device-independent quantum information protocols. We embed a tomographic complete set of measurement operators within the framework of a Bell sce…

Hedged maximum likelihood estimation

This paper proposes and analyzes a new method for quantum state estimation, called hedged maximum likelihood (HMLE). HMLE is a quantum version of Lidstone's Law, also known as the "add beta" rule. A straightforward modification of maximum likelihood estimation (MLE), it can be used as a plugin replacement for MLE. The HMLE estimate is a strictly positive density matrix, slightly less likely than the ML estimate, but with much better behavior for predictive tasks. Single-qubit numerics indicate that HMLE beats MLE, according to several metrics, for nearly all "true" states. For nearly-pure stat…