Quantum Secret Sharing Protocol Using Maximally Entangled Multi-qudit States

Abstract

The purpose of this paper is to develop a (N − k) threshold quantum secret sharing (QSS) scheme by using entangled multi-qudit states shared between N qudits such that (k ≤ N − k). We introduce first multi-qudit separable states of a Hilbert space associated with a disconnected multi-qudit system. The entangled multi-qudit states are obtained from disconnected states by means of a unitary interaction operator governing the evolution of the multi-qudit system, where the pairwise interaction establishes links between qudits. The generated entangled states are chosen to be maximally entangled with respect to a specific bi-partition ( $A_{2} \bigcup A_{1} $ ) with k = |A2|≤|A1| = (N − k) of the whole system such that the von Neumann entropy $S(\rho _{A_{2}})$ is maximal. The maximally entanglement property with respect to the splitting ( $A_{2} \bigcup A_{1} $ ) of this N-qudit entangled states will be used by a dealer (D) to share an encoded quantum secret with (N − 1) other players, such that at least the (N − k) specified players belonging to A1 have to cooperate jointly to get the complete information about the secret.