摘要
量子计算和量子通信是量子信息科学的两个重要组成部分.量子算法通常用到实系数等权重纯态,其中重要的一类是图态,图态的纠缠已经得到系统的研究.量子通信中不可避免地要用量子纠错码,其中最广泛使用的是与图态紧密相关的量子稳定子码,可以看作是由图态与经典编码两个要素构成的.本文将论证量子编码复杂度与量子码字纠缠的关系.为研究量子码字的纠缠,将证明几何测度、对数鲁棒纠缠和相对熵纠缠等纠缠测度对于量子稳定子码字而言是相等的,纠缠的上下界可由量子编码的生成元确定.用经典编码可以构造一类量子码,称为CSS码.其中最常用的是对偶包含法.对于CSS对偶包含码的码字,证明它的纠缠等于其经典生成元的个数.本文给出Gottesman码以及相关码的纠缠公式,还发展了迭代算法用来数值计算纠缠量.
Quantum communication and quantum computation are two important parts of quantum information science. Quantum algorithm usually uses real equally weighted states, among them are graph states, whose entanglement is well studied. Quantum communication is inevitably connected with quantum error correcting codes （QECC）. The most important and frequently used QECCs are quantum stabilizer codes, which can be seen as the combination of graph states with classical error correcting codes. We argue that the complexity of quantum coding is closely related to the entanglement of the code. We prove that entanglement measured by the geometric measure, the robustness and the relative entropy of entanglement are equal for a stabilizer quantum codeword. The entanglement upper and lower bounds are determined from the generators of a quantum code. CSS codes are quantum codes derived from classical codes. We prove that the entanglement of CSS code equals its number of classical generators when the CSS code is dual-containing. We give the entanglement of codewords for Gottesman codes and related codes. An iterative algorithm is developed to calculate the entanglement numerically.
出处
《中国科学：物理学、力学、天文学》
CSCD
北大核心
2015年第3期1-12,共12页
Scientia Sinica Physica,Mechanica & Astronomica
基金
国家自然科学基金资助项目(批准号:11375152
60972071)
关键词
量子编码
多组分纠缠
量子测量
quantum code, multipartite entanglement, entanglement measure
