Detecting $k$-nonseparability and $k$-partite Entanglement with Generalized Skew Information and Mutually Unbiased Measurements

TL;DR

This paper introduces new criteria based on generalized skew information and mutually unbiased measurements to detect $k$-nonseparability and $k$-partite entanglement in multipartite quantum systems, aiding quantum network analysis.

Contribution

It proposes novel sufficient criteria for entanglement detection using generalized skew information and mutually unbiased measurements, with practical examples and applications.

Findings

Effective detection of $k$-nonseparability demonstrated

Detection criteria outperform existing methods

Application to quantum network depth recognition

Abstract

Multipartite quantum entanglement, as a core quantum resource, is fundamental to the advancement of quantum science and technology. In multipartite quantum systems, there are two kinds of quantum entanglement: $k$-nonseparability and $k$-partite entanglement. In this paper, we propose sufficient criteria for detecting $k$-nonseparability and $k$-partite entanglement by using the generalized Wigner-Yanase skew information and mutually unbiased measurements. Examples are given to demonstrate the detection capability and advantages of these criteria. As an application, an example of recognizing the networks by detecting the depth of quantum networks is given.