Measuring multipartite entanglement efficiently by testing symmetries

TL;DR

This paper develops efficient symmetry-based methods to quantify multipartite entanglement, demonstrating their scalability and practical feasibility for large quantum systems through optimized sampling strategies.

Contribution

It introduces a family of symmetry test-based entanglement measures, along with near-optimal estimation techniques and analysis of their scalability for multipartite quantum states.

Findings

Sampling error scales as $O(N_{tot}^{-1/2})$, enabling feasible experiments.

Methods effectively compute entanglement measures for large quantum systems.

Asymptotic decay exponents are derived for states in many-body systems.

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.