Phase parameters of orthogonal arrays and special maximally multi-qubit entangled states

Quantum orthogonal arrays are combinatorial designs with a remarkable class of genuinely multipartite highly entangled states. In this paper, we propose the method for constructing maximally multi-qubit entangled state through phase parameters of orthogonal arrays. Using this method, we not only determine that maximally n-qubit entangled state, but also find the n − 1 orthogonal array that gives maximally n − 1 entangled states. Such states play an important role in quantum theory with a high degree of multipartite entanglement.