Applying the Theory of Numerical Radius of Operators to Obtain Multi-observable Quantum Uncertainty Relations  

作　　者：Kan HE Jin Chuan HOU 

机构地区：[1]College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,P.R.China [2]College of Information and Computer Science,Taiyuan University of Technology,Taiyuan 030024,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第7期1241-1254,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11771011,12071336)。

摘　　要：Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables(i.e.,bounded or unbounded self-adjoint operators).By revealing a connection between standard deviations of quantum observables and numerical radius of operators,we establish a universal uncertainty relation for k observables,of which the formulation depends on the even or odd quality of k.This universal uncertainty relation is tight at least for the cases k=2 and k=3.For two observables,the uncertainty relation is a simpler reformulation of Schr?dinger’s uncertainty principle,which is also tighter than Heisenberg’s and Robertson’s uncertainty relations.

关 键 词：Numerical radius of operators quantum uncertainty principle quantum observables quantum deviations 

分 类 号：O177[理学—数学] O413[理学—基础数学]