Quantum-Secret-Sharing Scheme Based on Local Distinguishability of Orthogonal Seven-Qudit Entangled States

The concept of judgment space was proposed by Wang et al. (Phys. Rev. A 95, 022320, 2017), which was used to study some important properties of quantum entangled states based on local distinguishability. In this study, we construct 15 kinds of seven-qudit quantum entangled states in the sense of permutation, calculate their judgment space and propose a distinguishability rule to make the judgment space more clearly. Based on this rule, we study the local distinguishability of the 15 kinds of seven-qudit quantum entangled states and then propose a (k, n) threshold quantum secret sharing scheme. Finally, we analyze the security of the scheme.