AI 中文总结
本文推广贝尔型检验，利用统计关联区分量子与经典时间演化，证明量子真空涨落产生独特关联，并区别于其他量子信号。
AI 中文摘要
贝尔不等式的违背为局部确定性系统中的非经典（量子）行为提供了明确的信号。然而，在许多预期量子力学发挥重要作用的物理场景中，人们无法利用现有的可观测量构建贝尔型检验。宇宙学提供了一个具体例子：宇宙结构可能起源于量子真空涨落，但所有观测实际上都是经典的。尽管如此，近期研究表明，量子和经典时间演化仍可通过这些可观测量的统计关联模式加以区分。在本文中，我们探索并推广了将关联用作时间演化性质的贝尔型检验。我们证明，经历哈密顿演化的封闭系统的量子真空涨落会产生独特的关联，这些关联不会被经典哈密顿系统所模仿。量子真空中的关联通常与时间无关，并由基态与激发态之间的能隙控制。经典系统在物理频率处表现出明显的极点，而这些极点不会出现在量子真空中。当接近极点时，演化由共振哈密顿量主导，从而产生随时间变化的关联，这些关联最终通过退相干而衰减。最后，我们证明这种行为与其他量子演化信号（包括量子光学、量子行走和量子搜索的应用）不同。
英文摘要
Violations of Bell's inequalities offer a definitive signal of non-classical (quantum) behavior in local deterministic systems. Yet, in many physical settings where quantum mechanics is expected to play an important role, one cannot construct a Bell-type test using the available observables. Cosmology offers one concrete example, where cosmic structure may have originated from quantum vacuum fluctuations yet all observations are effectively classical. Nevertheless, recent work suggests that quantum and classical time evolution may still be differentiated by the pattern of statistical correlations of these observables. In this paper, we explore and generalize the use of correlations as Bell-type test of the nature of time evolution. We show that quantum vacuum fluctuations of closed systems undergoing Hamiltonian evolution produce unique correlations that are not mimicked by classical Hamiltonian systems. Correlations in the quantum vacuum are generally time-independent and are controlled by the energy gap between the ground and exited states. Classical systems exhibit apparent poles at physical frequencies that do not arise in the quantum vacuum. As one approaches the poles, the evolution becomes dominated by a resonant Hamiltonian giving rise to time dependent correlations that eventually decay through dephasing. Finally, we show that this behavior is distinct from other signals of quantum evolution, including applications to quantum optics, quantum walks, and quantum search.
Comments60 pages, 1 figure
