HOW TO SHARE A QUANTUM SECRET

@article{Cleve1999HOWTS,
  title={HOW TO SHARE A QUANTUM SECRET},
  author={Richard Cleve and Daniel Gottesman and Hoi-Kwong Lo},
  journal={Physical Review Letters},
  year={1999},
  volume={83},
  pages={648-651}
}
We investigate the concept of quantum secret sharing. In a (k,thinspn) threshold scheme, a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the secret, but any set of k{minus}1 or fewer shares contains absolutely no information about the secret. We show that the only constraint on the existence of threshold schemes comes from the quantum {open_quotes}no-cloning theorem,{close_quotes} which requires that n{lt}2k , and we give efficient… 
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It is shown that any mixed state quantum secret sharing scheme can be derived by discarding a share from a pure state scheme, and that the size of each share in a quantumSecretSharing scheme must be at least as large as thesize of the secret.
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In the proposed schemes, the secret is recovered by communicating d d−k+1 qudits for every qudit of the secret, where d ≥ k, and it is shown that these schemes are optimal.
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