We introduce and analyse approximate quantum secret sharing in a formal cryptographic setting, wherein a dealer encodes and distributes a quantum secret to players such that authorized structures (sets of subsets of players) can approximately reconstruct the quantum secret and omnipotent adversarial agents controlling non-authorized subsets of players are approximately denied the quantum secret. In particular, viewing the map encoding the quantum secret to shares for players in an authorized structure as a quantum channel, we show that approximate reconstructability of the quantum secret by these players is possible if and only if the information leakage, given in terms of a certain entanglement-assisted capacity of the complementary quantum channel to the players outside the structure and the environment, is small.

翻译：我们引入并分析了形式化密码学设定下的近似量子秘密共享：其中，分发者将量子秘密编码并分发给参与者，使得授权结构（参与者子集的集合）能够近似重构该量子秘密，而控制非授权参与者子集的无所不能的对抗性代理无法近似获取该量子秘密。特别地，通过将编码量子秘密至授权结构中参与者份额的映射视为量子信道，我们证明：仅当以互补量子信道（面向该结构外参与者与环境）的某种纠缠辅助容量度量的信息泄漏足够小时，这些参与者才可能实现量子秘密的近似重构。