Entanglement has been recognized as being crucial when implementing various quantum information tasks. Nevertheless, quantifying entanglement for an unknown quantum state requires nonphysical operations or post-processing measurement data. For example, evaluation methods via quantum state tomography require vast amounts of measurement data and likely estimation. Although a direct entanglement determination has been reported for the unknown pure state, it is still tricky for the mixed state. In this work, assisted by weak measurement and deep learning technology, we directly detect the entanglement (namely, the concurrence) of a class of two-photon polarization-entangled mixed states both theoretically and experimentally according to the local photon spatial distributions after weak measurement. In this way, the number of projective bases is much smaller than that required in quantum state tomography.

中文翻译：

---

通过深度学习辅助的弱测量进行纠缠量化

在实施各种量子信息任务时，纠缠被认为是至关重要的。然而，量化未知量子态的纠缠需要非物理操作或后处理测量数据。例如，通过量子态断层扫描的评估方法需要大量的测量数据和可能的估计。尽管已经报道了未知纯态的直接纠缠测定，但对于混合态仍然很棘手。在这项工作中，我们借助弱测量和深度学习技术，根据弱测量后的局部光子空间分布，从理论上和实验上直接检测一类双光子偏振纠缠混合态的纠缠（即并发） 。这样，射影基数比量子态层析成像所需的要少得多。