Purity and Construction of Arbitrary Dimensional k $k$ -Uniform Mixed States

k-uniform mixed states are a significant class of states characterized by all k-party reduced states being maximally mixed.Novel methodologies are constructed for constructing k-uniform mixed states with the highest possible purity. By using the orthogonal partition of orthogonal arrays, a series of new k-uniform mixed states is derived. Consequently, an infinite number of higher-dimensional k-uniform mixed states, including those with highest purity, can be generated.