k -Uniform States in Heterogeneous Systems.

We study $k$ -uniform states in heterogeneous systems whose local dimensions are not all the same. Based on the connections between mixed orthogonal arrays with certain minimum Hamming distance, irredundant mixed orthogonal arrays and $k$ -uniform states, we present two constructions of 2-uniform states in heterogeneous systems. We also construct two families of 3-uniform states in heterogeneous systems, which solves a question posed in [D. Goyeneche et al., Phys. Rev. A 94, 012346 (2016)]. We show two methods of generating $(k-1)$ -uniform states from $k$ -uniform states. Some results on the nonexistence of absolutely maximally entangled states are provided. For the applications, we present an orthogonal basis consisting of $k$ -uniform states with the minimum support, and we show that some $k$ -uniform bases are locally irreducible. Moreover, we connect $k$ -uniform states with quantum information masking. [ABSTRACT FROM AUTHOR]