Assisted Quantum Secret Sharing
<|reference_start|>Assisted Quantum Secret Sharing: A restriction on quantum secret sharing (QSS) that comes from the no-cloning theorem is that any pair of authorized sets in an access structure should overlap. From the viewpoint of application, this places an unnatural constraint on secret sharing. We present a generalization, called assisted QSS (AQSS), where access structures without pairwise overlap of authorized sets is permissible, provided some shares are withheld by the share dealer. We show that no more than $\lambda-1$ withheld shares are required, where $\lambda$ is the minimum number of {\em partially linked classes} among the authorized sets for the QSS. This is useful in QSS schemes where the share dealer is honest by definition and is equivalent to a secret reconstructor. Our result means that such applications of QSS need not be thwarted by the no-cloning theorem.<|reference_end|>
@article{singh2004assisted,
    title={Assisted Quantum Secret Sharing},
    author={Sudhir Kumar Singh, R. Srikanth},
    journal={arXiv preprint arXiv:quant-ph/0407200},
    year={2004},
    archivePrefix={arXiv},
    eprint={quant-ph/0407200},
    primaryClass={quant-ph cs.CR math.CO}
}