We report here on the results of numerical searches for PPT states with specified ranks for density matrices and their partial transpose. The study includes several bipartite quantum systems of low dimensions. For a series of ranks extremal PPT states are found. The results are listed in tables and charted in diagrams. Comparison of the results for systems of different dimensions reveal several regularities. We discuss lower and upper bounds on the ranks of extremal PPT states.
翻译:我们在此报告对具有特定密度矩阵级及其部分转换的PPT国家进行数字搜索的结果。 研究包括几个低维的双边量子系统。 对于一系列的极端PPT状态,可以找到。 其结果列在图表中的表格和图表中。 对不同维度系统结果的比较显示了一些规律性。 我们讨论了极端PPT状态的上下限。