论文标题

通用重力校正的量子探针

Quantum probes for universal gravity corrections

论文作者

Candeloro, Alessandro, Boschi, Cristian Degli Esposti, Paris, Matteo G. A.

论文摘要

我们解决了重力理论产生的最小长度的估计。特别是,我们提供精确的界限,并评估量子探针的使用以增强估计性能。首先,我们回顾了最小长度的概念,并显示了它如何诱导任何量子系统的哈密顿量出现的扰动项,该量子系统与参数成正比,取决于最小长度。然后,我们系统地研究了这种扰动对几个一维系统不同状态准备的影响,并评估了量子Fisher信息,以便为任何估计程序的精确度找到最终的界限。最终,我们通过分析使用二维正方形井和谐波振荡器系统来探测最小长度来研究维数的作用。我们的结果表明,量子探针是方便的资源,可在精确度上提高潜在的增强。此外,我们的结果提供了一组指南,以设计可能的未来实验,以检测最小长度。

We address estimation of the minimum length arising from gravitational theories. In particular, we provide bounds on precision and assess the use of quantum probes to enhance the estimation performances. At first, we review the concept of minimum length and show how it induces a perturbative term appearing in the Hamiltonian of any quantum system, which is proportional to a parameter depending on the minimum length. We then systematically study the effects of this perturbation on different state preparations for several 1-dimensional systems, and we evaluate the Quantum Fisher Information in order to find the ultimate bounds to the precision of any estimation procedure. Eventually, we investigate the role of dimensionality by analysing the use of two-dimensional square well and harmonic oscillator systems to probe the minimal length. Our results show that quantum probes are convenient resources, providing potential enhancement in precision. Additionally, our results provide a set of guidelines to design possible future experiments to detect minimal length.

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