论量子统计推论

Quantum Statistical Inference

In this paper, inspired by the "Minimum Description Length Principle" in classical Statistics, we introduce a new method for predicting the outcomes of a quantum measurement and for estimating the state of a quantum system with minimum quantum complexity, while, at the same time, avoiding overfitting.

统计推断、量子态的可分辨性和量子纠缠

Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement

我们从统计推断的角度论证了量子相对熵是区分由密度矩阵描述的两个量子态（或两类量子态）的一个很好的度量。我们扩展了这个概念，从统计的角度来描述两个量子系统之间的纠缠量。我们的测量是独立的纠缠系统的数量和它们的维数。

什么时候一个输入状态总是比其他状态好？量子信道统计推断的普适最优输入态

When is an input state always better than the others ?: universally optimal input states for statistical inference of quantum channels

未知信道的统计估计和测试是近年来研究的热点。在优化推理过程中，一个重要的步骤是优化输入状态，这通常取决于推理的类型（估计或测试等），但有时，存在一个普遍最优的输入状态，或对所有的统计推断和所有的风险函数最好的输入状态。本文证明了群协变/逆变信道、单位量子比特信道和某些测量族的普遍最优状态的存在性。为了证明这些结果，我们使用了“状态族比较”的理论。我们还讨论了纠缠的有效性和输入态的自适应性。

Quantum Statistical Inference

In this thesis, I present several results on quantum statistical inference in the following two directions. Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a powerful model widely used in classical statistical inference and supervised machine learning. A crucial component of the quantum GP algorithm is solving linear systems with quantum computers, for which I present a novel algorithm that achieves a provable advantage over previously known methods. I will also explicitly address the task of encoding the classica…

非理想光子探测的统计推断

Statistical Inference from Imperfect Photon Detection

我们认为光子探测的统计特性与不完美的探测器，表现出暗计数和小于单位效率，在断层重建的背景下。在这种情况下，检测器用于实现某些POVM，其将允许重建所考虑的量子态或量子过程。在这里，我们看看从测量的结果频率推断结果概率的中间步骤，并显示如何在检测器缺陷的存在下以统计上合理的方式进行这种推断。将不同组POVM的结果概率合并到一致的量子态图像中已经在其他地方进行了处理[K.M.R. Audenaert和S. Scheel，New J.Phys.11，023028（2009）]。单光子脉冲测量以及连续波测量涵盖。

Geometric approach to quantum statistical inference

We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial differences which arise in the quantum regime in contrast to the classical setting. In our analysis, we primarily focus on the geometric approach to data inference problems, within which the aforementioned measures can be neatly interpreted as particular forms of divergences that quantify distances in the space of probability distributions or, when dealing wit…