Twopartite, combinatorial approach to partial k-separability problem for general multipartite states

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