We report here on the results of numerical searches for PPT states withspecified ranks for density matrices and their partial transpose. The studyincludes several bipartite quantum systems of low dimensions. For a series ofranks extremal PPT states are found. The results are listed in tables andcharted in diagrams. Comparison of the results for systems of differentdimensions reveal several regularities. We discuss lower and upper bounds onthe ranks of extremal PPT states.
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