Frérot Irénée, Roscilde Tommaso
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avenida Carl Friedrich Gauss 3, 08860 Barcelona, Spain.
Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany.
Phys Rev Lett. 2021 Jul 23;127(4):040401. doi: 10.1103/PhysRevLett.127.040401.
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.
多方纠缠是一种关键资源，它能使量子设备超越其经典对应物，而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，通常仅对特殊的纠缠态有效。在此，我们关注对量子态（以下称为量子数据）的有限测量集，并提出一种方法，给定感兴趣系统的特定空间划分，该方法能有效确定数据集是否与可分态兼容。当兼容性被证伪时，该方法会为手头的量子数据生成最优纠缠见证。我们的方法基于将可分态映射到晶格上的平衡经典场论，并将兼容性问题映射到一个逆统计问题，只要经典场论不描述玻璃态系统，就能在多项式时间内找到其解。我们的结果为量子设备中的系统纠缠认证铺平了道路，该认证针对可获取的可观测量进行了优化。
