Some Directions beyond Traditional Quantum Secret Sharing

Details Some Directions beyond Traditional Quantum Secret Sharing Some Directions beyond Traditional Quantum Secret Sharing

2008-05-07

arxiv.org/abs/0805.1076v1

Physics

Quantum Physics

To appear in Physica Scripta, 7 pages, 1 figure, subsumes arXiv:quant-ph/0407200

Scientific paper

10.1088/0031-8949/77/06/065007

We investigate two directions beyond the traditional quantum secret sharing (QSS). First, 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 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. 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 a 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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