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

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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.

uncertainty relationthe tightest uncertainty constantsoptimal observable sets

Xiao-Bin Liang、Bo Li、Shao-Ming Fei

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School of Mathematics and Computer Science,Shangrao Normal University,Shangrao 334001,China

Quantum Information Research Center,Shangrao Normal University Shangrao 334001,China

School of Mathematical Sciences,Capital Normal University Beijing 100048,China

National Natural Science Foundation of China(NSFC)National Natural Science Foundation of China(NSFC)National Natural Science Foundation of China(NSFC)National Natural Science Foundation of China(NSFC)

12065021120751591217104412175147

2024

10.1007/s11433-024-2409-7

中国科学:物理学 力学 天文学(英文版)
中国科学院

中国科学:物理学 力学 天文学(英文版)

CSTPCD
影响因子：0.91
ISSN：1674-7348
年,卷(期)：2024.67(9)