arXiv 2511.075372025-11-10quant-ph

通过对称性检验高效测量多体纠缠

Measuring multipartite entanglement efficiently by testing symmetries

Xiaoyu Liu, Jordi Tura, Albert Rico

AI总结：

本文提出利用量子对称性检验构建两体及多体纠缠度量，给出高效估计方法与近最优采样策略，并证明采样误差按总副本数负二分之一次方缩放，兼具实验可行性与实际应用价值。

摘要：

近年来，一种被称为量子对称性检验的技术在探测纯量子态中的两体纠缠方面受到越来越多的关注。在本工作中，我们证明除了定性检测之外，还可以通过对称性检验获得一族定义良好的两体和多体纠缠度量。我们提出并对几种估计这些度量的高效方法进行了基准测试，并为每种方法推导出近最优的采样策略。尽管这些方法具有非线性，我们证明采样误差随总副本数 $N_{\mathrm{tot}}$ 的缩放不差于 $O(N_{\mathrm{tot}}^{-1/2})$，这表明其具有实验可行性。通过利用对称性，我们计算了大量副本下的这些度量，并推导出多体系统中相关态的渐近衰减指数。利用这些结果，我们识别出所提出的纠缠度量在估计复杂性与灵敏度之间的权衡，并面向实际实现进行了设计。

英文摘要：

Recently, a technique known as quantum symmetry test has gained increasing attention for detecting bipartite entanglement in pure quantum states. In this work we show that, beyond qualitative detection, a family of well-defined measures of bipartite and multipartite entanglement can be obtained with symmetry tests. We propose and benchmark several efficient methods to estimate these measures, and derive near-optimal sampling strategies for each. Despite the nonlinearity of the methods, we demonstrate that the sampling error scales no worse than $O(N_{\mathrm{tot}}^{-1/2})$ with the total number of copies $N_{\mathrm{tot}}$, which suggests experimental feasibility. By exploiting symmetries we compute our measures for large number of copies, and derive the asymptotic decay exponents for relevant states in many-body systems. Using these results we identify tradeoffs between estimation complexity and sensitivity of the presented entanglement measures, oriented to practical implementations.

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