Detection of genuine entanglement for multipartite quantum states

We study genuine multipartite entanglement of arbitrary n -partite quantum states by representing the density matrices in terms of generalized Pauli operators. While the usual Bloch representation of a density matrix uses three types of generators in the special unitary Lie algebra 𝔰𝔲(d) , the Weyl representation with generalized Pauli operators has one uniformed type of generators that simplifies computation. In this paper, we take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement. We also generalize the results to obtain a sufficient criterion to detect genuine entanglement for multipartite quantum states in arbitrary dimensions. The new method can detect more genuine entangled states than previous methods as backed by detailed examples.