AI 中文总结
本文提出一种基于三阶局域随机测量的有限尺寸纠缠认证方法，利用维度无关的集中界控制有限样本误差，以较低开销揭示二阶测量无法检测的纠缠。
AI 中文摘要
认证高维系统中的纠缠通常需要完整的态层析，其成本随系统维度快速增长。局域随机测量提供了一种可扩展的替代方案，但现有的基于二阶关联的测试仅能获取关于状态的有限信息。在此，我们推导出一种有限尺寸纠缠证书，将局域随机测量扩展到三阶。额外的三阶信息揭示了在二阶时仍未被检测到的纠缠，同时一个与维度无关的集中界为有限样本误差提供了严格的控制。我们的结果为从实验平台提取更强的纠缠信息开辟了一条实用途径，而无需承担态层析随维度增长的开销。
英文摘要
Certifying entanglement in high-dimensional systems usually requires full state tomography, whose cost grows rapidly with the system dimension. Local randomized measurements offer a scalable alternative, but existing tests based on second-order correlations access only limited information about the state. Here, we derive a finite-size entanglement certificate that extends local randomized measurements to third order. The additional third-order information reveals entanglement that remains undetected at second order, while a dimension-independent concentration bound provides rigorous control of finite-sample errors. Our result opens a practical route to extracting stronger entanglement information from experimental platforms without the dimension-dependent overhead of state tomography.
CommentsPreviously this version appeared as arXiv:2604.13165 which was submitted as a new work by accident. Any subsequent updates will appear there
