Better Entanglement Witness for Genuine Multipartite Entanglement

In the short contribution, we consider inequalities of confirming genuine multipartite entanglement. We have a better entanglement witness for a particular mixed state to test genuine multipartite entanglement. Our physical situation is that we measure Pauli observables σ x , σ y , and σ z per side. If the reduction factor is greater than 0.4, then we can confirm the measured quantum state is genuine multipartite entangled experimentally.