The information rate is an important metric of the performance of a secret-sharing scheme. In this paper we consider 272 non-isomorphic connected graph access structures with nine vertices and eight or nine edges, and either determine or bound the optimal information rate in each case. We obtain exact values for the optimal information rate for 231 cases and present a method that is able to derive information-theoretical upper bounds on the optimal information rate. Moreover, we apply some of the constructions to determine lower bounds on the information rate. Regarding information rate, we conclude with a full listing of the known optimal information rate （or bounds on the optimal information rate） for all 272 graphs access structures of nine participants.
In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimensional quantum system by making use of the majorization technique; these uncertainty relations are then generalized to mixed states. We find that the lower bounds are always nonnegative for pure states but may be negative for some mixed states. Second, the quantum uncertainty relations for single qubit states are obtained by the analytical method. We show that the lower bounds obtained by this technique are always positive for single qubit states. Third, the lower bounds obtained by the two methods described above are compared for single qubit states.
如何构造针对一般存取结构的理想的多秘密共享方案是一个比较困难的问题.本文首先解决了Spiez等最近提出的一个公开问题[Finite Fields and Their Application,2011,17:329–342],即在特权数组存在的前提下,设计求得任意长度的特权数组的算法.进一步,我们利用特权数组理论,以Pang等和Yang等的方案为例,分析了大多现有的基于Shamir门限体制的多秘密共享方案均不是完善的.最后,基于特权数组的算法,本文提出了一个多秘密共享方案,我们证明了该方案是理想的,并且方案的存取结构中的授权集比门限方案的更加丰富.
