Measuring multipartite entanglement efficiently by testing symmetries

• URL: http://arxiv.org/abs/2511.07537v1
• Date: Wed, 12 Nov 2025 01:02:34 GMT
• Title: Measuring multipartite entanglement efficiently by testing symmetries
• Authors: Xiaoyu Liu, Jordi Tura, Albert Rico,
• Abstract summary: We show that a family of well-defined measures of bipartite and multipartite entanglement can be obtained with symmetry tests.<n>We propose and benchmark several efficient methods to estimate these measures, and derive near-optimal sampling strategies for each.
• Score: 3.995502708329505
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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