On the non-$k$-separability of Dicke class of states and $N$-qudit W states

TL;DR

This paper develops criteria to detect non-$k$-separability and genuine multipartite entanglement in complex quantum states, demonstrating their effectiveness on Dicke and W states, and showing they are experimentally feasible.

Contribution

The paper introduces new separability criteria for multipartite states that are applicable to higher-dimensional systems and can be implemented with local measurements.

Findings

Criteria successfully detect non-$k$-separability in Dicke and W states.

Criteria are robust against white noise.

Implementation with local observables is feasible.

Abstract

In this paper, we present the separability criteria to identify non-$k$-separability and genuine multipartite entanglement in mixed multipartite states using elements of density matrices. Our criteria can detect the non-$k$-separability of Dicke class of states, anti W states and mixtures thereof and higher dimensional W class of states. We then investigate the performance of our criteria by considering $N$-qubit Dicke states with arbitrary excitations added with white noise and mixture of $N$-qudit W state with white noise. We also study the robustness of our criteria against white noise. Further, we demonstrate that our criteria are experimentally implementable by means of local observables such as Pauli matrices and generalized Gell-Mann matrices.