量子密码协议分析与设计的图演算方法

项目名称： 量子密码协议分析与设计的图演算方法

项目编号： No.61003212

项目类型： 青年科学基金项目

立项/批准年度： 2011

项目学科： 金属学与金属工艺

项目作者： 王全龙

作者单位： 北京航空航天大学

项目金额： 7万元

中文摘要： 范畴论在计算机科学中有着广泛的应用，它能以结构的方式揭示概念的本质。范畴量子力学是将范畴论应用于量子力学所得到的理论，其自2004年提出以来已经取得了丰硕的成果。本项目在范畴量子力学的框架下研究了一类基本的量子密码协议-量子秘密分享协议。我们给出了该协议的范畴结构刻画并证明其正确性，还分析了其安全性。同时我们把该协议推广到更一般的情形，即任意基于双代数测量的量子秘密分享协议。进一步，我们发现对量子秘密分享协议的正确性证明可以转换为对非定域性的Mermin论据的证明。这为将量子信息与计算的方法应用于基础物理的研究作了有益的尝试。

中文关键词： 范畴量子力学；量子秘密分享；非定域性；对称monoidal范畴

英文摘要： Category theory has been widely used in computer science, which characterizes the essential of a concept by structures. Since it was proposed in 2004, categorical quantum mechanics has obtained a lot of important results, as an application of category theory to quantum mechanics. This project studied a basic type of quantum cryptographical protocols, i.e., quantum secret sharing protocols , within the framework of categorical quantum mechanics. We give the categorical structure of this protocol and prove its correctness, as well as analyzing its security. Moreover, we generalize this protocol to more general case, i.e. quantum secret sharing based on bi-algebraic measurements. Furthermore, we find that the correctness proof of quantum secret sharing can be converted to Mermin argument on non-locality proof, which open the door for applying results from quantum information and computation to fundamental physics.

英文关键词： categorical quantum mechanics; quantum secret sharing; non-locality; symmetric monoidal category