Using a recently introduced framework, we derive criteria for quantum k-separability, which are easily computed. In the case k=2, our criteria are equally strong to the best methods known so far, while in all other cases there are currently no comparable criteria known. We also show how the criteria can be implemented experimentally.
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.
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 describe a general methods to localize any sort of k-separability and therefore also the corresponding partial entanglement in genuinely multipartite mixed quantum states. Our methods are based exclusively on the known twopartite methods and some systematic procedures of combinatorial nature. Our methods are formalized in an algorithmic-like fashion and therefore they are easily implementable in a computer environments and might be effectively used for studying numerically these questions for sufficiently small systems