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An inherently infinite-dimensional quantum correlation

Coladangelo, Andrea and Stark, Jalex (2020) An inherently infinite-dimensional quantum correlation. Nature Communications, 11 . Art. No. 3335. ISSN 2041-1723.

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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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Coladangelo, Andrea0000-0002-6773-2711
Additional Information:© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit Received 23 November 2019; Accepted 08 June 2020; Published 03 July 2020. The authors thank Laura Mančinska, William Slofstra. and Thomas Vidick for useful discussions. The authors also thank Thomas Vidick for valuable comments on an earlier version of this paper. A.C. is supported by the Kortschak Scholars program and AFOSR YIP award number FA9550-16-1-0495. J.S. is supported by NSF CAREER Grant CCF-1553477 and the Mellon Mays Undergraduate Fellowship. Author Contributions: Both authors contributed extensively to this work and to the writing of this manuscript. The authors declare no competing interests.
Funding AgencyGrant Number
Kortschak Scholars ProgramUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0495
Andrew W. Mellon FoundationUNSPECIFIED
Subject Keywords:Quantum information; Theoretical physics
Record Number:CaltechAUTHORS:20200713-100418370
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Official Citation:Coladangelo, A., Stark, J. An inherently infinite-dimensional quantum correlation. Nat Commun 11, 3335 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104352
Deposited By: Tony Diaz
Deposited On:13 Jul 2020 17:23
Last Modified:13 Jul 2020 17:23

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