On quantum evolving schemes (pp385-407)
          S. S. Chaudhury
          doi: https://doi.org/10.26421/QIC22.5-6-2
Abstracts: A quantum secret sharing scheme is a method to share a quantum  secret among participants in such a way that only certain specified subsets of the set of participants can combine to recover the secret. A quantum evolving secret sharing scheme is a recently introduced variant of secret sharing schemes where the sets of participants is not fixed and an unbounded and unspecified number of  participants arrive one by one with time. The number of participants can be potentially infinite and and a quantum secret is shared and protected among the participants. The existing construction has some major drawbacks such as 1) the exponential quantum memory requirement and 2) the very high dimensions  of the shares   which makes the scheme difficult to implement. In this paper we overcome these drawbacks by constructing a scheme which uses  quantum memory linear in the number of participants and significantly improves on the dimensions of the shares of the participants. This construction uses quantum secret redistribution and trap codes. The construction is flexible and can be modified to different types of access structures(subsets of participants which can recover the secret). Certain ramp properties can also be incorporated in the scheme.
Key Words: Quantum Evolving Secret Sharing, Trap Code, Quantum Secret Redistribution, Quantum Threshold Secret Sharing