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(National Laboratory of Solid State Microstructures,College of Engineering and Applied Sciences and School of Physics,Nanjing University,Nanjing 210093,China;Collaborative Innovation Center of Advanced Microstructures,Nanjing University,Nanjing 210093,China;Department of Computer Science and Technology,Tsinghua University,Beijing 100084,China;Shenzhen Institute for Quantum Science and Engineering and Department of Physics,Southern University of Science and Technology,Shenzhen 518055,China;Shenzhen Key Laboratory of Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen 518055,China;Institute for Quantum Information&State Key Laboratory of High Performance Computing,College of Computer,National University of Defense Technology,Changsha 410073,China;Centre for Quantum Software and Information,School of Software,Faculty of Engineering and Information Technology,University of Technology Sydney,NSW,Australia)

机构地区：[1]National Laboratory of Solid State Microstructures,College of Engineering and Applied Sciences and School of Physics,Nanjing University,Nanjing 210093,China [2]Collaborative Innovation Center of Advanced Microstructures,Nanjing University,Nanjing 210093,China [3]Department of Computer Science and Technology,Tsinghua University,Beijing 100084,China [4]Shenzhen Institute for Quantum Science and Engineering and Department of Physics,Southern University of Science and Technology,Shenzhen 518055,China [5]Shenzhen Key Laboratory of Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen 518055,China [6]Institute for Quantum Information&State Key Laboratory of High Performance Computing,College of Computer,National University of Defense Technology,Changsha 410073,China [7]Centre for Quantum Software and Information,School of Software,Faculty of Engineering and Information Technology,University of Technology Sydney,NSW,Australia

出　　处：《Chinese Physics Letters》2021年第7期11-16,共6页中国物理快报（英文版）

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.

摘　　要：As a foundation of quantum physics,uncertainty relations describe ultimate limit for the measurement uncertainty of incompatible observables.Traditionally,uncertainty relations are formulated by mathematical bounds for a specific state.Here we present a method for geometrically characterizing uncertainty relations as an entire area of variances of the observables,ranging over all possible input states.We 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 momentum.Moreover,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 sets.In 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.

关 键 词：OBSERVABLE UNION OPERATORS 

分 类 号：O413[理学—理论物理]