量子纠缠表征及其实验研究

量子纠缠是量子技术发展的核心资源，判定和度量纠缠是量子领域的基本问题。现在已经有多种判定纠缠的充分或必要条件，但通常需要已知态的信息，对未知态难以适用。此外，为了探究纠缠的产生机制和内部结构，也需要能够直接度量纠缠大小的方法。目前能够精确度量纠缠的方法都需要量子态的完整信息，依赖于量子态层析（Full Quantum State Tomography，FQST）技术。但是FQST的方法会随系统规模的增加，测量所需的次数呈指数增长，因此不适合用于测量多体系统的纠缠。 为了降低FQST的复杂度，人们提出了多种方法，但它们难以保证精确度，因为相近的态可能有显著不同的纠缠值。本文提出了两种无需态重构的纠缠测量方法，第一种方法是通过搭建参数化量子线路（Parameterized Quantum Circuit，PQC）来对角化量子态，进而估计用来计算纠缠的特征值。第二种方法是利用机器学习的方法，训练好的神经网络不仅能够直接从局域测量信息给出静态纠缠信息，而且经验证，机器学习的方法能够预测训练时间以外的超长时间的纠缠动力学。此外，本文还在核磁共振平台上进行了实验验证，充分展示了这两种方法的实际可行性。

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