Criteria for non-$k$-separability of $n$-partite quantum states

TL;DR

This paper introduces new criteria based on density matrix elements to identify non-$k$-separability and genuine multipartite entanglement in mixed $n$-partite quantum states, with potential for experimental realization.

Contribution

It develops novel separability criteria for detecting non-$k$-separability and multipartite entanglement in mixed quantum states using density matrix elements.

Findings

Successfully detect non-$k$-separability in noisy GHZ and W states.

Propose experimental implementation via local observables.

Enhance understanding of entanglement structure in complex quantum systems.

Abstract

We develop separability criteria to identify non-$k$-separability $(k = 2,3,\ldots,n)$ and genuine multipartite entanglement in different classes of mixed $n$-partite quantum states using elements of density matrices. With the help of these criteria, we detect non-$k$-separability in $n$-qudit GHZ and W states respectively added with white noise. We also discuss the experimental implementation of our criteria by means of local observables.