量子计算模型的判定性、无歧量子通信及相关问题

项目名称： 量子计算模型的判定性、无歧量子通信及相关问题

项目编号： No.60873055

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 无线电电子学、电信技术

项目作者： 邱道文

作者单位： 中山大学

项目金额： 31万元

中文摘要： 本项目研究量子计算模型的判定性问题，特别是讨论任意两个双向量子有限自动机之间是否等价的判定性问题；对任意两个量子下推自动机识别的语言，研究它们的交是否为空及它们是否相等的判定性问题。同时，研究基于量子逻辑的计算理论（正交模格值自动机）中的判定性问题。另一重要问题是考虑无歧量子通信。在这种通信方式中，Bob解码出来的信息一定是与原信息相符的，但是Bob可能以一定的概率忽略Ailce传来的信息，即输出"不知道"。在无歧义量子通信的意义下，我们研究Bob成功解码Alice传来信息的概率的最优界，并澄清双方共享的纠缠在这类通信模型中的作用。量子通信中的另一个问题是量子混合态的区分，所以我们澄清有歧区分的最小误差概率与无歧区分的失败概率之间的关系。最后在量子逻辑、剩余格值逻辑和其它代数框架下，我们系统地研究一些推理模型。

中文关键词： 量子计算模型；量子通信；判定性；量子逻辑；剩余格

英文摘要： In this project, we investigate the decidability issues concerning quantum computing models, and, in particular, we deal with the decidability of equivalence of arbitrary two two-way quantum finite automata. For the languages recognized by any two quantum pushdown automata, we discuss the decidability of whether their intersection is empty. Also, we study the decidability in the theory of computation based on quantum logic (i.e., orthomodular lattice-valued automata). On the other hand, we consider unambiguous quantum communication. In this fashion of communication, Bob can exactly decode the information transmitted by Alice with a certain probability, but Bob may also omit the information received with a certain probability, that is, he may give an answer of "not knowing" with a certain probability. We study the optimal upper bound on the probability of Bob successfully decoding the information from Alice, and we clarify the role of entanglement shared by both in this way of communication. Another issue related to quantum communication is regarding the discrimination of mixed states. Therefore, we clarify the relation between the minimun-error probability of ambiguous discrimination and the failure probability of unambiguous discrimination. Finally, we investigate some reasoning models in the framework of quantum logic, residuated lattice-valued logic and other algebras.

英文关键词： Quantum computing models; quantum communication; decidability; quantum logic; residuated lattices