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

Abstract 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.