Detection of the quantum states containing at most $k-1$ unentangled particles

TL;DR

This paper develops new entanglement criteria to identify quantum states with at most $k-1$ unentangled particles, improving detection effectiveness through inequality-based methods and concrete examples.

Contribution

It introduces novel inequality-based criteria for detecting specific entanglement classes in multipartite quantum states, enhancing previous methods.

Findings

Criteria effectively identify states with at most $k-1$ unentangled particles

Concrete examples demonstrate improved detection performance

New inequalities outperform existing methods in certain cases

Abstract

There are many different classifications of entanglement for multipartite quantum systems, one of which is based on the number of unentangled particles. In this paper, we mainly study the quantum states containing at most $k-1$ unentangled particles and provide several entanglement criteria based on different forms of inequalities which can both identify quantum states containing at most $k-1$ unentangled particles. We show that these criteria are more effective for some states by concrete examples.