Threshold quantum secret sharing using graph states of prime-dimensional systems

Secret sharing schemes allow a classical or quantum secret to be divided among many parties such that it can be recovered only by some specified set of parties collaborating in order to do so. It is known that arbitrary secret sharing schemes may be constructed by concatenating threshold schemes, in which the secret can be recovered by any sufficiently large number of parties, and the remainder are denied any knowledge of the secret I will discuss a formalism within which, using entangled graph states of prime-dimensional systems, a variety of different threshold secret sharing schemes (involving both quantum and classical secrets and quantum and classical channels shared between parties) may be unified. I will give explicit protocols for three varieties of secret sharing within this formalism, including some for which the analogous formalism using graph states of two-dimensional systems is not sufficient.