Quantum k -Uniform States From Quantum Orthogonal Arrays

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called k -uniform states whose every reductions to k parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength 2 with levels of prime power, as well as some constructions of strength 3. As a consequence, we give infinite classes of 2-uniform states of N systems with dimension of prime power d ≥ 2 for arbitrary N ≥ 5; 3-uniform states of N -qubit systems for arbitrary N ≥ 6 and N ≠ 7,8,9,11; 3-uniform states of N systems with dimension of prime power d ≥ 7 for arbitrary N ≥ 7.