Improved criteria of detecting multipartite entanglement structure

TL;DR

This paper introduces improved criteria and algorithms for detecting and characterizing multipartite entanglement structures, such as entanglement depth and stretchability, in large quantum systems, enhancing verification methods in quantum information.

Contribution

It proposes a systematic method using tensor product partitions and efficient algorithms to better identify multipartite entanglement structures than existing techniques.

Findings

New entanglement witnesses outperform previous criteria

Efficient semi-definite programming algorithm detects entanglement structures

Demonstrated effectiveness on detailed quantum system examples

Abstract

Multipartite entanglement is one of the crucial resources in quantum information processing tasks such as quantum metrology, quantum computing and quantum communications. It is essential to verify not only the multipartite entanglement, but also the entanglement structure in both fundamental theories and the applications of quantum information technologies. However, it is proved to be challenging to detect the entanglement structures, including entanglement depth, entanglement intactness and entanglement stretchability, especially for general states and large-scale quantum systems. By using the partitions of the tensor product space we propose a systematic method to construct powerful entanglement witnesses which identify better the multipartite entanglement structures. Besides, an efficient algorithm using semi-definite programming and a gradient descent algorithm are designed to detect entanglement structure from the inner polytope of the convex set containing all the states with the same entanglement structure. We demonstrate by detailed examples that our criteria perform better than other known ones. Our results may be applied to many quantum information processing tasks.