Coladangelo Andrea, Stark Jalex
Computing and Mathematical Sciences, Caltech, USA.
Nat Commun. 2020 Jul 3;11(1):3335. doi: 10.1038/s41467-020-17077-9.
Bell's theorem, a landmark result in the foundations of physics, establishes that quantum mechanics is a non-local theory. It asserts, in particular, that two spatially separated, but entangled, quantum systems can be correlated in a way that cannot be mimicked by classical systems. A direct operational consequence of Bell's theorem is the existence of statistical tests which can detect the presence of entanglement. Remarkably, certain correlations not only witness entanglement, but they give quantitative bounds on the minimum dimension of quantum systems attaining them. In this work, we show that there exists a correlation which is not attainable by quantum systems of any arbitrary finite dimension, but is attained exclusively by infinite-dimensional quantum systems (such as infinite-level systems arising from quantum harmonic oscillators). This answers the long-standing open question about the existence of a finite correlation witnessing infinite entanglement.
贝尔定理是物理学基础领域的一个里程碑式成果，它表明量子力学是一种非定域理论。特别地，它断言两个空间分离但纠缠的量子系统能够以一种经典系统无法模拟的方式产生关联。贝尔定理的一个直接实际结果是存在能够检测纠缠存在的统计检验。值得注意的是，某些关联不仅能见证纠缠，还能对达到这些关联的量子系统的最小维度给出定量界限。在这项工作中，我们表明存在一种关联，它无法被任意有限维度的量子系统实现，而只能由无限维量子系统（例如由量子谐振子产生的无限能级系统）唯一实现。这回答了关于存在见证无限纠缠的有限关联这一长期存在的开放性问题。
