两类近似无偏基的新构造

中国民航大学学报 ›› 2022, Vol. 40 ›› Issue (6): 60-64.

• 基础科学 • 上一篇

两类近似无偏基的新构造

徐登明^a，李非亚^b

（中国民航大学a.中欧航空工程师学院；b.理学院，天津300300）

收稿日期:2021-01-22 修回日期:2021-04-27 出版日期:2022-12-10 发布日期:2023-10-26
作者简介:徐登明（1981—），男，贵州铜仁人，副教授，博士，研究方向为量子信息中的数学问题.

New construction of two kinds of approximate unbiased bases

XU Dengming^a , LI Feiya^b

(a. Sino-European Institute of Aviation Engineering; b. College of Science, CAUC, Tianjin 300300, China)

Received:2021-01-22 Revised:2021-04-27 Online:2022-12-10 Published:2023-10-26

摘要/Abstract

摘要： 相互无偏基构造是量子通信理论中一个重要的研究内容。一般情况下，确定有限维复向量空间上相互无偏基的最大组数十分困难，因此放松了内积条件的近似无偏基逐渐被考虑。目前，构造近似无偏基最有效的工具是指数和，本文利用有限域上的两种指数和，构造了两类新的近似无偏基。

关键词: 近似无偏基, 有限域, 高斯和, 雅克比和

Abstract: Mutually unbiased bases are the main topics in quantum information theory. In general, it is difficult to determine the maximal number of mutually unbiased bases over a finite dimensional complex vector space. For this reason, mutually unbiased bases with relaxed inner product conditions, the so called approximately mutually unbiased bases, have been gradually considered. Exponential sums over finite fields play an important role in the construction of approximately mutually unbiased bases. In this paper, two new approximately mutually unbiased bases are constructed using two kinds of exponential sums over finite fields.

Key words: approximately mutually unbiased bases, finite field, Gauss sums, Jacobi sums

中图分类号:

O413

徐登明, 李非亚. 两类近似无偏基的新构造[J]. 中国民航大学学报, 2022, 40(6): 60-64.

XU Dengming , LI Feiya. New construction of two kinds of approximate unbiased bases[J]. Journal of Civil Aviation University of China, 2022, 40(6): 60-64.

参考文献

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两类近似无偏基的新构造

New construction of two kinds of approximate unbiased bases

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