Refining recent results, we propose an upper bound for the norms of Bloch Vectors for heterogeneous quantum systems containing an arbitrary number of qudits with possibly different numbers of levels. We also generalize recent approaches for tripartite and four-partite heterogeneous systems and for multipartite homogeneous systems. Our results imply a necessary algebraic condition for separability of a general multipartite heterogeneous quantum system under arbitrary partitioning.

中文翻译：

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使用Bloch向量的异构多部分量子系统的可分性

为了完善最近的结果，我们为异构量子系统的Bloch向量范数的上限提出了上限，该异构量子系统包含任意数量的qudits，并且可能具有不同数量的能级。我们还概括了三方和四方异构系统以及多方均质系统的最新方法。我们的结果暗示了在任意划分下一般多部分异质量子系统可分性的必要代数条件。