Graph states and ramp schemes for quantum secret sharing

I will discuss our recent work in developing new protocols for quantum secret sharing (QSS), a cryptographic scheme in which an encoded quantum "secret" is divided between several "players" such that only certain subsets of players may recover it. We have found a class of protocols based on graph states which allow for efficient (i.e. player states of the same dimension as the secret) QSS for states of prime dimension. We have also found examples of "ramp" schemes for QSS, in which the efficiency can be improved by sacrificing some security. I will discuss these and the use of shared entanglement as a measure of the players' information about the secret.