熵不确定度关系综述  

Review on entropic uncertainty relations

作　　者：李丽娟[1] 明飞 宋学科 叶柳[1] 王栋[1] Li Li-Juan;Ming Fei;Song Xue-Ke;Ye Liu;Wang Dong(School of Physics and Optoelectronics Engineering,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学物理与光电工程学院,合肥230601

出　　处：《物理学报》2022年第7期19-35,共17页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12075001,61601002,12004006,12175001);安徽省自然科学基金(批准号:1508085QF139);中国科学院量子信息重点实验室开放基金(批准号:No.KQI201701)资助的课题。

摘　　要：不确定关系是量子力学的基本特征之一,随着量子信息理论的蓬勃发展,不确定关系更是在其中发挥着重要的作用.特别是将熵引入来描述不确定关系之后,不确定关系在量子信息技术中涌现出多种应用.众所周知,熵不确定度关系已成为几乎所有量子密码协议安全分析的核心要素.这篇综述主要回顾不确定关系的发展历史和最新研究进展,从Heisenberg提出不相容测量其结果是不能被预测伊始,许多学者在该观点的启发下,做了进一步的相关扩展研究,将可观测物体与环境之间的量子关联结合起来,对不确定关系进行各种推广从而得到更普适的数学表达式.除此以外,本文还重点介绍了量子存储下的熵不确定度关系及其发展,也介绍了在某些物理系统中对应的动力学特性.最后讨论了熵不确定度关系在量子信息领域的各种应用,从随机数到波粒二象性再到量子密钥分发.The Heisenberg uncertainty principle is one of the characteristics of quantum mechanics.With the vigorous development of quantum information theory,uncertain relations have gradually played an important role in it.In particular,in order to solved the shortcomings of the concept in the initial formulation of the uncertainty principle,we brought entropy into the uncertainty relation,after that,the entropic uncertainty relation has exploited the advantages to the full in various applications.As we all know the entropic uncertainty relation has became the core element of the security analysis of almost all quantum cryptographic protocols.This review mainly introduces development history and latest progress of uncertain relations.After Heisenberg’s argument that incompatible measurement results are impossible to predict,many scholars,inspired by this viewpoint,have made further relevant investigations.They combined the quantum correlation between the observable object and its environment,and carried out various generalizations of the uncertainty relation to obtain more general formulas.In addition,it also focuses on the entropy uncertainty relationship and quantum-memoryassisted entropic uncertainty relation,and the dynamic characteristics of uncertainty in some physical systems.Finally,various applications of the entropy uncertainty relationship in the field of quantum information are discussed,from randomnesss to wave-particle duality to quantum key distribution.

关 键 词：熵不确定度关系 量子存储 量子关联 

分 类 号：O413.1[理学—理论物理]