Signifying quantum uncertainty relations by optimal observable sets and the tightest uncertainty constants  

作　　者：Xiao-Bin Liang Bo Li Shao-Ming Fei 

机构地区：[1]School of Mathematics and Computer Science,Shangrao Normal University,Shangrao 334001,China [2]Quantum Information Research Center,Shangrao Normal University,Shangrao 334001,China [3]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2024年第9期43-50,共8页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(NSFC)(Grant Nos.12065021,12075159,12171044,and 12175147)。

摘　　要：Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical observables.Here,we introduce the concept of optimal observable sets and define the tightest uncertainty constants to accurately describe these measurement uncertainties.For any quantum state,we establish optimal sets of three observables for both product and summation forms of uncertainty relations,and analytically derive the corresponding tightest uncertainty constants.We demonstrate that the optimality of these sets remains consistent regardless of the uncertainty relation form.Furthermore,the existence of the tightest constants excludes the validity of standard real quantum mechanics,underscoring the essential role of complex numbers in this field.Additionally,our findings resolve the conjecture posed in[Phys.Rev.Lett.118,180402(2017)],offering novel insights and potential applications in understanding preparation uncertainties.

关 键 词：uncertainty relation the tightest uncertainty constants optimal observable sets 

分 类 号：O413.1[理学—理论物理]