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引用次数: 0
摘要
量子不确定性关系制约着多个非交换量子力学观测变量的测量精度。在此,我们引入了最优观测值集的概念,并定义了最严格的不确定性常数,以准确描述这些测量不确定性。对于任何量子态,我们都能为不确定性关系的乘积和求和形式建立三个观测值的最优集,并通过分析推导出相应的最严格不确定性常数。我们证明,无论不确定关系形式如何,这些集合的最优性都是一致的。此外,最严格常数的存在排除了标准实量子力学的有效性,强调了复数在这一领域的重要作用。此外,我们的发现解决了[Phys. Rev. Lett. 118, 180402 (2017)]中提出的猜想,为理解制备不确定性提供了新的见解和潜在应用。
Signifying quantum uncertainty relations by optimal observable sets and the tightest uncertainty constants
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.
Science China Physics, Mechanics & Astronomy, is published in both print and electronic forms. It is indexed by Science Citation Index.
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