Generalizing Quantum Secret Sharing Using Secure Carriers

We generalize the secret sharing scheme of reference [1] to more general access structures, namely a large class of (k, n) threshold schemes. The basic property of our scheme and that of [1] is that the entanglement is not used as a resource, but can be re-generated after each round of the protocol by suitable unitary operations of all the dealers. In effect an entangled state shared between all the participants plays the role of a carrier to which information is hooked by the sender and unhooked by the legitimate parties, by suitable operations. In view of the high cost of entanglement generation, our scheme may find useful applications in the future.

[1] Saber Bagherinezhad, Vahid Karimipour, Quantum secret sharing based on reusable GHZ states as secure carriers Physical Rev. A 67, 044302 (2003).