An inherently infinite-dimensional quantum correlation

• Published in: Nature communications Vol. 11; no. 1; pp. 3335 - 6
• Main Authors: Coladangelo, Andrea, Stark, Jalex
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 03.07.2020; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/483/481; 639/766/483/640; Correlation; Existence theorems; Games; Harmonic oscillators; Humanities and Social Sciences; multidisciplinary; Oscillators; Probability; Quantum entanglement; Quantum mechanics; Quantum physics; Science; Science (multidisciplinary); Statistical analysis; Statistical tests
• ISSN: 2041-1723; 2041-1723
• 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. The existence of nonlocal correlations which cannot be attained exactly by finite-dimensional systems, but can be attained by infinite-dimensional ones, has been the subject of several theoretical efforts. Here, Coladangelo and Stark exhibit such a correlation, in a form that requires only two players.