High-efficient quantum secret sharing with arrangements of lines on two-dimensional planes

摘要

We investigate a simple (2, 2)-threshold scheme and its generalised (n, n)-threshold scheme for the quantum secret sharing (QSS) based on fundamental laws of analytic geometry. The dealer aptly selects the possible Greenberger-Horne-Zeilinger (GHZ) states related to the coefficients which determine the characteristics of straight lines on the same two-dimensional plane. By judging whether two lines intercept or not, we obtain a judging matrix whose rank can be used for determining the secret stored in entangled states. With the aid of the database technology, the authorised participant accesses to the database and achieves the useful information, where the secret never appears in the noisy channel. It is shown that the eavesdropper fails to obtain any secret by applying the individual attack strategy.