Some Directions beyond Traditional Quantum Secret Sharing

TL;DR

This paper introduces assisted quantum secret sharing (AQSS), relaxing the no-cloning constraint by allowing withheld shares, and explores combining quantum secret sharing with quantum key distribution for shared classical information.

Contribution

It generalizes QSS to include non-overlapping authorized sets via withheld shares and links QSS security to QKD, broadening application possibilities.

Findings

AQSS allows non-overlapping authorized sets with withheld shares.

No more than λ-1 shares need to be withheld, where λ is the number of partially linked classes.

Security of certain QSS schemes can be reduced to QKD security.

Abstract

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.