有噪声纠缠比特的纠缠辅助量子纠错码研究

项目名称： 有噪声纠缠比特的纠缠辅助量子纠错码研究

项目编号： No.11471011

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 李瑞虎

作者单位： 中国人民解放军空军工程大学

项目金额： 75万元

中文摘要： 纠缠辅助量子纠错码假设收信方的纠缠比特不受噪声影响，而实际量子系统中噪声是不可避免的。收信方的纠缠比特受噪声影响的纠缠辅助量子纠错码叫做有噪声纠缠辅助量子纠错码。本项目研究有噪声纠缠辅助量子纠错码的数学理论框架、构造方法以及性能分析等问题。首先研究如何建立稳定子形式的有噪声纠缠辅助量子纠错码的理论框架，利用稳定子与辛子空间以及加性码的联系，给出有噪声纠缠辅助量子码的数学形式；其次讨论由纠缠辅助量子码和标准量子码构成的组合编码的特征与构造；进而探讨一般有噪声纠缠辅助量子码的构造方法，构造出性能超过标准量子码、参数优良的有噪声纠缠辅助量子码；最后，分析有噪声纠缠辅助量子纠错码的信道可靠度，从资源节省、信道可靠度高低等角度比较不同编码方案的优劣及适用场合。通过上述研究揭示有噪声纠缠辅助量子纠错码的内在规律，为有噪声纠缠辅助量子纠错码应用于实际量子通信、量子计算和量子密码学提供理论依据。

中文关键词： 量子纠错码；纠缠辅助；有噪声纠缠比特；加性码；信道可靠度

英文摘要： The scheme of entanglement-assisted quantum error-correcting codes (EAQECCs) assumes that the ebits of the receiver are noise-free. In practical situations, noises on these ebits are unavoidable. EAQECCs with noisy ebits are called noisy EAQECCs.This project aims at studying mathematical formalism of noisy EAQECCs, constructions of noisy EAQECCs and analysizing performance of them. Firstly, we consider how to establish stabilizer formalism of noisy EAQECs, then set up relations among stabilizers, symplectic spaces and additive codes, and give mathematical forms of noisy EAQECCs. Secondly, we discuss characteristics of combination code which is composed of an EAQECC and a standard QECC, and manage to construct this special kind of noisy EAQECCs.Thirdly, we try to find new mathematical methods for constructing genaral noisy EAQECCs and construct noisy EAQECCs with good parameters and are better than standard quantum error-correcting codes. At last, we study channel fidelety of noisy EAQECCs, analysis performance of different noisy EAQECCs from view points of resource useage and fidelety, and choose the best EAQECCs to use in practice. By solving the previous peoblems, we can reveal intrinsic rules of noisy EAQECCs, and provide theoretical basis for practical applications of noisy EAQECC in quantum communication, quantum computation and quantum cryptography.

英文关键词： quantum error-correcting code;entanglement-assisted;noisy ebit;additive code;channel fidelity