Reducing the quantum communication cost of quantum secret sharing

We demonstrate a new construction for perfect quantum secret sharing (QSS) schemes based on imperfect "ramp" secret sharing combined with classical encryption, in which the individual parties' shares are split into quantum and classical components, allowing the former to be of lower dimension than the secret itself. We show that such schemes can be performed with smaller quantum components and lower overall quantum communication than required for existing methods. We further demonstrate that one may combine both imperfect quantum and imperfect classical secret sharing to produce an overall perfect QSS scheme, and that examples of such scheme (which we construct) can have the smallest quantum and classical share components possible for their access structures, something provably not achievable using perfect underlying schemes. Our construction has significant potential for being adapted to other QSS schemes based on stabiliser codes.