[HTML][HTML] An inherently infinite-dimensional quantum correlation

A Coladangelo, J Stark - Nature communications, 2020 - nature.com
Nature communications, 2020nature.com
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 …
Abstract
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.
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