Detection of $k$-partite entanglement and $k$-nonseparability of multipartite quantum states

TL;DR

This paper introduces new, simple inequalities for detecting $k$-partite entanglement and $k$-nonseparability in multipartite quantum states, outperforming existing criteria and applicable in current experiments.

Contribution

The authors develop and demonstrate powerful, easy-to-implement criteria for identifying various levels of entanglement and nonseparability in $N$-partite quantum systems, improving detection capabilities.

Findings

Criteria outperform existing detection methods.

Able to detect previously unrecognized entanglement.

Applicable with current experimental techniques.

Abstract

Identifying the $k$-partite entanglement and $k$-nonseparability of general $N$-partite quantum states are fundamental issues in quantum information theory. By use of computable inequalities of nonlinear operators, we present some simple and powerful $k$-partite entanglement and $k$-nonseparability criteria that works very well and allow for a simple and inexpensive test for the whole hierarchy of $k$-partite entanglement and $k$-separability of $N$-partite systems with $k$ running from $N$ down to 2. We illustrate their strengths by considering several examples in which our criteria perform better than other known detection criteria. We are able to detect $k$-partite entanglement and $k$-nonseparabilty of multipartite systems which have previously not been identified. In addition, our results can be implemented in today's experiments.