Quantum secret sharing by high-dimensional systems

Abstract

Secret sharing is a cryptographic system such that authorized people share secret messages and their cooperation is required to retrieve the whole message. A quantum protocol for secret sharing was proposed by Hillery et al. [M. Hillery, V. Buzek, and A. Berthiaume, Phys. Rev. A 59, 1829 (1999)] and employs two-dimensional systems. We generalize the protocol to high dimensional systems. For that purpose, we utilize the perfect quantum correlation of entanglement among the subsystems. We show that high dimensionality leads to large transmission rates in sharing secret information and provides better security than the two-dimensional protocol.