We derive a combinatorial criterion for detecting k-separability of N-partite Dicke states. The criterion is efficiently computable and implementable without full state tomography. We give examples in which the criterion succeeds, where known criteria fail.
The k-separability of mixed n-partite (n≥3) quantum states is mainly discussed in this paper. We obtain practical k-separability criteria to identify k-nonseparable mixed multipartite states in arbitrary dimensional quantum systems and detect genuine n-partite entanglement (k=2) and entanglement (k=3) which have previously not been identified. No optimization or eigenvalue evaluation is needed, our criteria can be evaluated by simple computations involving components of the density matrix and can be implemented in today's experiments.
Detection of k-nonseparable n-partite quantum states
The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful k-separability criteria of mixed n-partite (n≥3) quantum states to detect k-nonseparable n-partite quantum states. Our criteria can be expressed by the elements of the density matrix, which allows a simple and practical evaluation and computation. They are experimentally accessible without quantum state tomography.
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.
Abstract We study separability in arbitrary multipartite quantum systems based on principal base matrices. Necessary conditions are presented for different kinds of separable states. These conditions can give a complete classification of multipartite quantum states. While the usual Bloch representation of a density matrix uses three types of generators, the representation with principal base matrices has one uniform type of generator which simplifies computation. In this paper, we take advantage of this simplicity to derive useful and operational criteria to detect multipartite separability. We first obtain criteria on detecting 1 − 3 separable, 2 − 2 separable, 1 − 1 − 2 separable and fully separable four-partite quantum states. We then study k-separability for multipartite quantum states in arbitrary dimensions. Detailed examples are given to show that our criteria are able to detect more entanglement states than some existing criteria.