Some directions beyond traditional quantum secret sharing

We investigate two directions beyond the traditional quantum secret sharing (QSS). Firstly, a restriction on 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 are permissible, provided some shares are withheld by the share dealer. We show that no more than λ−1 withheld shares are required, where λ is the minimum number of partially linked classes among the authorized sets for the QSS. Our result means that such applications of QSS need not be thwarted by the no-cloning theorem. Secondly, we point out a way of combining the features of QSS and quantum key distribution (QKD) for applications where classical information is shared by quantum means. We observe that in such case, it is often possible to reduce the security proof of QSS to that of QKD.

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