A Unified Toolbox for Multipartite Entanglement Certification

TL;DR

This paper introduces a unified framework using the conditional gradient method for efficient multipartite entanglement certification, capable of handling complex quantum states and noise, with practical scalability demonstrated up to ten qubits.

Contribution

It develops a versatile, scalable approach combining heuristic detection and rigorous witness construction for multipartite entanglement analysis, extending capabilities beyond previous methods.

Findings

Successfully certifies entanglement in systems of up to ten qubits.

Closes the gap between entanglement and separability bounds in noise robustness tests.

Extends entanglement robustness analysis to general quantum noise channels.

Abstract

We present a unified framework for multipartite entanglement characterization based on the conditional gradient (CG) method, incorporating both fast heuristic detection and rigorous witness construction with numerical error control. Our method enables entanglement certification in quantum systems of up to ten qubits and applies to arbitrary entanglement structures. We demonstrate its power by closing the gap between entanglement and separability bounds in white noise robustness benchmarks for a class of bound entangled states. Furthermore, the framework extends to entanglement robustness under general quantum noise channels, providing accurate thresholds in cases beyond the reach of previous algorithmic methods. These results position CG methods as a powerful tool for practical and scalable entanglement analysis in realistic experimental settings.