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

TL;DR

This paper introduces a combinatorial, algorithmic approach to identify k-separability and partial entanglement in complex multipartite quantum states, leveraging existing bipartite methods for effective numerical analysis.

Contribution

It presents a novel, systematic method combining bipartite techniques with combinatorial procedures to analyze partial separability in multipartite quantum states.

Findings

Method effectively localizes k-separability in multipartite states

Algorithmic approach is implementable in computational environments

Applicable to small quantum systems for numerical studies

Abstract

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