Constructing a Maximally Entangled Seven-Qubit State via Orthogonal Arrays

Huber et al. Phys. Rev. Lett. 118 (2017) 200502 have proved that a seven-qubit state whose three-body marginal states are all maximally mixed does not exist. Here, we propose a method to build a maximally entangled state based on orthogonal arrays to construct maximally entangled seven-qubit states. Using this method, we not only determine that a seven-qubit state whose three-body marginals are all maximally mixed does not exist, but also find the condition for maximally entangled seven-qubit states. We consider that \pi_\rm ME =19/140 is a condition for maximally entangled seven-qubit states. Furthermore, we derive three forms of maximally entangled seven-qubit states via orthogonal arrays.