We derive hierarchies of separability criteria that identify the different degrees of entanglement ranging from bipartite to genuine multipartite in mixed quantum states of arbitrary size.
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.
Monogamy of bipartite correlations leads, for arbitrary pure multiqubit states, to simple conditions able to indicate various types of multipartite entanglement by being capable of excluding the possibility of k separability.
Necessary conditions for classifying m-separability of multipartite entanglements
We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our criteria are simple functions of the given quantum state and detect genuine multipartite entanglement that had not been identified so far. They are experimentally accessible without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed.