Incompatibility of observables as state-independent bound of uncertainty relations

Xiao，Yunlong1,2,3; Guo，Cheng4; Meng，Fei1,5; Jing，Naihuan6,7; Yung，Man Hong1,8,9

2019-09-23

10.1103/PhysRevA.100.032118

Physical Review A   影响因子和分区

2469-9926

2469-9934

For a pair of observables, they are called "incompatible" if and only if their commutator does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the incompatibility among three or more observables? Here, we explore one possible route towards this goal through uncertainty relations, which impose fundamental constraints on the measurement precisions for incompatible observables. Specifically, we propose to measure the incompatibility by the optimal state-independent bounds of additive variance-based uncertainty relations. In this way, the degree of incompatibility becomes an intrinsic property among the operators, i.e., state independent. In particular, we focus on the incompatibility of spin-1/2 systems as an illustration. For an arbitrary, including nonorthogonal, setting of a finite number Pauli-spin operators, the incompatibility is analytically solved; the spins are maximally incompatible if and only if they are orthogonal to each other. On the other hand, our measure of incompatibility represents a versatile tool for applications such as testing the entanglement of bipartite states, and EPR-steering criteria.

SCI ; EI

英语

第一

Simons Foundation[198129] ; Simons Foundation[523868]

Optics ; Physics

Optics ; Physics, Atomic, Molecular & Chemical

WOS:000487724100004

AMER PHYSICAL SOC

20194107508776

Uncertainty analysis

Probability Theory:922.1 ; Quantum Theory; Quantum Mechanics:931.4

PHYSICS

2-s2.0-85072922316

Scopus

1.Shenzhen Institute for Quantum Science and Engineering and Department of PhysicsSouthern University of Science and Technology,Shenzhen,518055,China
2.Institute for Quantum Science and Technology and Department of Mathematics and StatisticsUniversity of Calgary,Calgary,T2N IN4,Canada
3.Max Planck Institute for Mathematics in the Sciences,Leipzig,04103,Germany
4.Institute for Advanced StudyTsinghua University,Beijing,100084,China
5.Department of Computer ScienceUniversity of Hong Kong,Pokfulam Road,Hong Kong
6.Department of MathematicsShanghai University,Shanghai,200444,China
7.Department of MathematicsNorth Carolina State University,Raleigh,27695,United States
8.Shenzhen Key Laboratory of Quantum Science and EngineeringSouthern University of Science and Technology,Shenzhen,518055,China
9.Central Research InstituteHuawei Technologies,Shenzhen,518129,China

Xiao，Yunlong,Guo，Cheng,Meng，Fei,et al. Incompatibility of observables as state-independent bound of uncertainty relations[J]. Physical Review A,2019,100(3).

Xiao，Yunlong,Guo，Cheng,Meng，Fei,Jing，Naihuan,&Yung，Man Hong.(2019).Incompatibility of observables as state-independent bound of uncertainty relations.Physical Review A,100(3).

Xiao，Yunlong,et al."Incompatibility of observables as state-independent bound of uncertainty relations".Physical Review A 100.3(2019).