Multipartite entanglement is a key resource allowing quantum devices to outperform their classical counterparts, and entanglement certification is fundamental to assess any quantum advantage. The only scalable certification scheme relies on entanglement witnessing, typically effective only for special entangled states. Here, we focus on finite sets of measurements on quantum states (hereafter called quantum data), and we propose an approach which, given a particular spatial partitioning of the system of interest, can effectively ascertain whether or not the dataset is compatible with a separable state. When compatibility is disproven, the approach produces the optimal entanglement witness for the quantum data at hand. Our approach is based on mapping separable states onto equilibrium classical field theories on a lattice and on mapping the compatibility problem onto an inverse statistical problem, whose solution is reached in polynomial time whenever the classical field theory does not describe a glassy system. Our results pave the way for systematic entanglement certification in quantum devices, optimized with respect to the accessible observables.

中文翻译：

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最佳纠缠见证：一种可扩展的数据驱动方法

多方纠缠是一种关键资源，使量子设备能够超越经典设备，纠缠认证是评估任何量子优势的基础。唯一可扩展的认证方案依赖于纠缠见证，通常仅对特殊纠缠状态有效。在这里，我们专注于量子态的有限测量集（以下称为量子数据），并且我们提出了一种方法，该方法在给定感兴趣系统的特定空间分区的情况下，可以有效地确定数据集是否与可分离的数据集兼容。状态。当兼容性被否定时，该方法会为手头的量子数据生成最佳纠缠见证。我们的方法基于将可分离状态映射到格子上的平衡经典场论，并将兼容性问题映射到逆统计问题，只要经典场论不描述玻璃系统，就可以在多项式时间内达到该问题的解。我们的结果为量子设备中的系统纠缠证明铺平了道路，并针对可访问的可观察量进行了优化。