Neat trick from separability buisiness for arriving at arbitrary rank with a lower rank technique

What is it about?

I recursively employ the technique for the estimation of the convex roof for rank two density matrix up to density matrices of arbitrary rank. The method is applied to the transverse Ising model and some benchmark states for which exact results are known.

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Why is it important?

This work demonstrates how one can employ every estimation procedure at hand to estimate the convex roof of density matrices of arbitrary rank from above. Other numerical implementations work on a merely statistical fashion. Together with algorithms for lower rank, this will approach as much closer to the exact convex roof as more techniques for higher rank matrices are available.