{"title":"Signifying quantum uncertainty relations by optimal observable sets and the tightest uncertainty constants","authors":"Xiao-Bin Liang, Bo Li, Shao-Ming Fei","doi":"10.1007/s11433-024-2409-7","DOIUrl":null,"url":null,"abstract":"<div><p>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. <b>118</b>, 180402 (2017)], offering novel insights and potential applications in understanding preparation uncertainties.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":null,"pages":null},"PeriodicalIF":6.4000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science China Physics, Mechanics & Astronomy","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11433-024-2409-7","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
Science China Physics, Mechanics & Astronomy, an academic journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China, and published by Science China Press, is committed to publishing high-quality, original results in both basic and applied research.
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