Generalized Semi-Quantum Secret Sharing Schemes - Vlad Gheorghiu

I will show that any stabilizer quantum error correcting code induces a generalized quantum secret sharing scheme with an access structure, a forbidden structure and an intermediate one. I will prove that the access structure completely determines the other two, and provide an explicit algorithm for determining the former. I next show that the information available to the intermediate structure can be fully quantified and described by an information group, a subgroup of the Pauli group, and employ this group structure to construct a method for hiding the information from the intermediate structure via twirling of the information group and sharing of classical bits between the dealer and the players. This scheme allows the transformation of a ramp (intermediate) quantum secret sharing scheme into a semi-quantum threshold secret sharing scheme, and is optimal in the amount of classical communication required between the dealer and the players. I will illustrate the main concepts by simple examples.