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.

Automated summary

This paper studies genuine multipartite entanglement of arbitrary n-partite quantum states by using generalized Pauli operators. The Weyl representation with these operators simplifies computation and allows for the derivation of useful criteria for detecting genuine tripartite entanglement. The results are generalized to detect genuine entanglement in multipartite quantum states of arbitrary dimensions, and examples demonstrate its effectiveness in detecting more genuine entangled states than previous methods.