  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.
