论文标题
通过人工神经网络估算与WEHRL矩的纠缠量的几何测量
Estimation of the geometric measure of entanglement with Wehrl Moments through Artificial Neural Networks
论文作者
论文摘要
近年来，人工神经网络（ANN）已成为研究量子理论（尤其是纠缠理论）中问题的越来越流行的工具。在这项工作中，我们仅使用有限数量的WEHRL矩（状态的Husimi功能的力矩）将ANN在多大程度上准确地预测对称多Quebit状态的几何测量，以代表有关状态的部分信息。我们认为纯量子和混合量子状态。我们将训练ANN获得的结果与融合加速方法的知情使用进行比较。我们发现，即使给出相同的输入数据时，即使是一些最强大的收敛加速算法也不会与ANN竞争，但前提是可以使用足够的数据来训练这些ANN。我们还提供了一个实验方案，用于测量与国家无关的WEHRL力矩。更一般而言，这项工作为估算纠缠措施和其他SU（2）以上的数量（例如WEHRL熵）开辟了观点，其在实验中比通过全州层析成像更容易访问的方式。
In recent years, artificial neural networks (ANNs) have become an increasingly popular tool for studying problems in quantum theory, and in particular entanglement theory. In this work, we analyse to what extent ANNs can accurately predict the geometric measure of entanglement of symmetric multiqubit states using only a limited number of Wehrl moments (moments of the Husimi function of the state) as input, which represents partial information about the state. We consider both pure and mixed quantum states. We compare the results we obtain by training ANNs with the informed use of convergence acceleration methods. We find that even some of the most powerful convergence acceleration algorithms do not compete with ANNs when given the same input data, provided that enough data is available to train these ANNs. We also provide an experimental protocol for measuring Wehrl moments, which is state-independent. More generally, this work opens up perspectives for the estimation of entanglement measures and other SU(2)-invariant quantities, such as the Wehrl entropy, in a way that is more accessible in experiments than by means of full state tomography.
