Detection of $k$-nonseparable $n$-partite quantum states

TL;DR

This paper develops practical criteria based on density matrix elements for detecting $k$-nonseparable $n$-partite quantum states, enabling easier experimental identification of multipartite entanglement without full state tomography.

Contribution

It introduces new $k$-separability criteria for mixed $n$-partite quantum states that are simple to evaluate and do not require quantum state tomography.

Findings

Criteria are expressed via density matrix elements.

Criteria are experimentally accessible.

Effective for detecting $k$-nonseparable states.

Abstract

The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful $k$-separability criteria of mixed $n$-partite ($n\geq 3$) quantum states to detect $k$-nonseparable $n$-partite quantum states. Our criteria can be expressed by the elements of the density matrix, which allows a simple and practical evaluation and computation. They are experimentally accessible without quantum state tomography.