Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays to heterogeneous multipartite systems with different individual levels. The second is the existence of k-uniform states in heterogeneous quantum systems. We present explicit constructions of two- and three-uniform states for arbitrary heterogeneous multipartite systems with coprime individual levels and characterize the entangled states in heterogeneous systems consisting of subsystems with nonprime power dimensions as well. Moreover, we obtain infinite classes of k-uniform states for heterogeneous multipartite systems for any \(k\ge 2\). The non-existence of a class of IrMOAs is also proved.

量子多部分纠缠态在量子信息处理中起着重要作用。通过使用差分方案和正交分区，我们构造了一系列无限类的冗余混合正交数组（IrMOA），从而为两个开放问题提供了肯定的答案。第一个是将构造同构系统的方法从正交数组扩展到具有不同单个层的异构多部分系统的方法。第二是k的存在异质量子系统中的均匀态。我们提出了具有互素个体水平的任意异构多部分系统的两统一状态和三统一状态的显式构造，并表征了由具有非初等幂维数的子系统组成的异构系统中的纠缠态。此外，对于任何\（k \ ge 2 \），我们为异构多部分系统获得k-一致状态的无限类。一类IrMOA的不存在也被证明。