两体系统上的无偏不可扩展最大纠缠基

Constructions of mutually unbiased unextendible maximally entangled bases

摘要

量子纠缠在量子计算与量子信息处理中扮演着关键角色,然而其内在性质与数学结构至今尚未得到完整的刻画.相互无偏性作为描述量子纠缠的重要工具之一,近年来受到广泛关注.基于傅里叶矩阵和组合构型,在两体量子系统C^d⊗C^d'(d<d')构造出两组相互无偏的不可扩展最大纠缠基,其中d'是奇素数.

Abstract

Quantum entanglement plays a crucial role in quantum computing and quantum information processing.However,its intrinsic nature and mathematical structure have not yet been fully characterized.Mutual unbiasedness,as one of the important tools for describing quantum entanglement,has received widespread attention in recent years.Based on Fourier matrices,we construct two sets of mutually unbiased unextendible maximally entangled biased in bipartite quantum systems C^d⊗C^d'(d<d'),where d' is an odd prime number.

关键词

两体量子系统 / 傅里叶矩阵 / 施密特系数 / 不可扩展最大纠缠基 / 相互无偏基

Key words

bipartite quantum systems / Fourier matrices / Schmidt number / unextendible maximally entangled bases / mutually unbiased bases

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基金资助

国家自然科学基金(12571493)

国家自然科学基金(62272208)

石家庄市驻冀高校基础研究项目(241790697A)

河北师范大学科研基金资助项目(L2025J01)

网络与交换技术全国重点实验室(北京邮电大学)开放课题资助项目(SKLNST-2025-1-19)