Entirety of Quantum Uncertainty and Its Experimental Verification

作     者：Jie Xie Li Zhou Aonan Zhang Huichao Xu Man-Hong Yung Ping Xu Nengkun Yu Lijian Zhang 谢杰;周立;张傲男;徐慧超;翁文康;徐平;俞能昆;张利剑

作者机构：National Laboratory of Solid State MicrostructuresCollege of Engineering and Applied Sciences and School of PhysicsNanjing UniversityNanjing 210093China Collaborative Innovation Center of Advanced MicrostructuresNanjing UniversityNanjing 210093China Department of Computer Science and TechnologyTsinghua UniversityBeijing 100084China Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and TechnologyShenzhen 518055China Shenzhen Key Laboratory of Quantum Science and EngineeringSouthern University of Science and TechnologyShenzhen 518055China Institute for Quantum Information&State Key Laboratory of High Performance ComputingCollege of ComputerNational University of Defense TechnologyChangsha 410073China Centre for Quantum Software and InformationSchool of SoftwareFaculty of Engineering and Information TechnologyUniversity of Technology SydneyNSWAustralia 

出 版 物：《Chinese Physics Letters》 (中国物理快报（英文版）)

年 卷 期：2021年第38卷第7期

页      面：11-16页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：Supported by the National Key Research and Development Program of China(Grant No.2017YFA0303703) the National Natural Science Foundation of China(Grant Nos.91836303,61975077,61490711,11690032,11875160,and U1801661) the Natural Science Foundation of Guangdong Province(Grant No.2017B030308003) the Key R&D Program of Guangdong Province(Grant No.2018B030326001) the Science,Technology and Innovation Commission of Shenzhen Municipality(Grant Nos.JCYJ20170412152620376,JCYJ20170817105046702,and KYTDPT20181011104202253) the Economy,Trade and Information Commission of Shenzhen Municipality(Grant No.201901161512) Guangdong Provincial Key Laboratory(Grant No.2019B121203002) ARC DECRA 180100156 and ARC DP210102449 

主　　题：observable union operators 

摘      要：As a foundation of quantum physics,uncertainty relations describe ultimate limit for the measurement uncertainty of incompatible ***,uncertainty relations are formulated by mathematical bounds for a specific *** we present a method for geometrically characterizing uncertainty relations as an entire area of variances of the observables,ranging over all possible input *** find that for the pair of position and momentum operators,Heisenberg s uncertainty principle points exactly to the attainable area of the variances of position and ***,for finite-dimensional systems,we prove that the corresponding area is necessarily semialgebraic;in other words,this set can be represented via finite polynomial equations and inequalities,or any finite union of such *** particular,we give the analytical characterization of the areas of variances of(a)a pair of one-qubit observables and(b)a pair of projective observables for arbitrary dimension,and give the first experimental observation of such areas in a photonic system.