We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient
k-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems. These criteria can be used to distinguish
n−1 different classes of multipartite inseparable states and can detect many important multipartite entangled states such as GHZ states, W states, anti W states, and mixtures thereof. They detect
k-nonseparable
n-partite quantum states which have previously not been identified. Here
k=2,3,⋯,n. No optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. Most importantly, they can be implemented in today's experiments by using at most
O(n2) local measurements.
We investigate the detection of entanglement in
n-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and nonseparable mixed quantum states. No numerical optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. We provide examples in which our criteria perform better than all known separability criteria. Specifically, we are able to detect genuine
n-partite entanglement which has previously not been identified. In addition, our criteria can be used in today's experiments.
We derive a hierarchy of separability criteria for multimode continuous-variable systems. They permit one to study in a unified way the
k-partite entanglement of broad classes of Gaussian and non-Gaussian states. With specific examples we demonstrate the strength of the criteria, and we discuss their assessment based on data obtained from Gaussian measurements.