Abstract
Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical ob-servables.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 prod-uct 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.
基金项目
National Natural Science Foundation of China(NSFC)(12065021)
National Natural Science Foundation of China(NSFC)(12075159)
National Natural Science Foundation of China(NSFC)(12171044)
National Natural Science Foundation of China(NSFC)(12175147)
万方数据