Entirety of Quantum Uncertainty and Its Experimental Verification

Xie, Jie1,2,3; Zhou, Li4; Zhang, Aonan1,2,3; Xu, Huichao1,2,3; Yung, Man-Hong5,6,7; Xu, Ping1,2,3,8,9; Yu, Nengkun10; Zhang, Lijian1,2,3

2021-07-01

10.1088/0256-307X/38/7/070303

CHINESE PHYSICS LETTERS   影响因子和分区

0256-307X

1741-3540

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.

SCI ; EI

英语

其他

National Key Research and Development Program of China[2017YFA0303703] ; National Natural Science Foundation of China[91836303,61975077,61490711,11690032,11875160,"U1801661"] ; Natural Science Foundation of Guangdong Province[2017B030308003] ; Key R&D Program of Guangdong Province[2018B030326001] ; Science, Technology and Innovation Commission of Shenzhen Municipality["JCYJ20170412152620376","JCYJ20170817105046702","KYTDPT20181011104202253"] ; Economy, Trade and Information Commission of Shenzhen Municipality[201901161512] ; Guangdong Provincial Key Laboratory[2019B121203002] ; ARC DECRA[180100156] ; ARC[DP210102449]

Physics

Physics, Multidisciplinary

WOS:000681459400001

IOP PUBLISHING LTD

20220711660939

Polynomials

Algebra:921.1 ; Probability Theory:922.1

PHYSICS

Web of Science

1.Nanjing Univ, Coll Engn & Appl Sci, Natl Lab Solid State Microstruct, Nanjing 210093, Peoples R China
2.Nanjing Univ, Sch Phys, Nanjing 210093, Peoples R China
3.Nanjing Univ, Collaborat Innovat Ctr Adv Microstruct, Nanjing 210093, Peoples R China
4.Tsinghua Univ, Dept Comp Sci & Technol, Beijing 100084, Peoples R China
5.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
6.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
7.Southern Univ Sci & Technol, Shenzhen Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China
8.Natl Univ Def Technol, Coll Comp, Inst Quantum Informat, Changsha 410073, Peoples R China
9.Natl Univ Def Technol, Coll Comp, State Key Lab High Performance Comp, Changsha 410073, Peoples R China
10.Univ Technol Sydney, Fac Engn & Informat Technol, Sch Software, Ctr Quantum Software & Informat, Sydney, NSW, Australia

Xie, Jie,Zhou, Li,Zhang, Aonan,et al. Entirety of Quantum Uncertainty and Its Experimental Verification[J]. CHINESE PHYSICS LETTERS,2021,38(7).

Xie, Jie.,Zhou, Li.,Zhang, Aonan.,Xu, Huichao.,Yung, Man-Hong.,...&Zhang, Lijian.(2021).Entirety of Quantum Uncertainty and Its Experimental Verification.CHINESE PHYSICS LETTERS,38(7).

Xie, Jie,et al."Entirety of Quantum Uncertainty and Its Experimental Verification".CHINESE PHYSICS LETTERS 38.7(2021).