Genuine multipartite entanglement (GME) offers more significant advantages in quantum information compared with entanglement. We propose a sufficient criterion for the detection of GME based on local sum uncertainty relations for chosen observables of subsystems. We apply the criterion to detect the GME properties of noisy
n-partite W state when
n=3,4,5 and
6, and find that the criterion can detect more noisy W states when
n ranges from 4 to 6. Moreover, the criterion is also used to detect the genuine entanglement of
3-qutrit state. The result is stronger than that based on GME concurrence and fisher information.
We study the genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria.