An inherently infinite-dimensional quantum correlation

Andrea Coladangelo,Jalex Stark

doi:10.1038/s41467-020-17077-9

Andrea Coladangelo, Jalex Stark

Open Access

https://doi.org/10.1038/s41467-020-17077-9

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Journal: Nature Communications	Publication Date: Jul 3, 2020
Citations: 5	License type: open-access

Affiliation: California Institute of Technology

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.

Highlights

Bell’s theorem, a landmark result in the foundations of physics, establishes that quantum mechanics is a non-local theory
Certain correlations witness the presence of entanglement, but they provide quantitative bounds on the minimum dimension of quantum systems that attain them
One of the most natural questions one can ask about a correlation is “in which models of physics can the correlation be realized?” The example of the CHSH game shows that while certain correlations can be realized in classical physics, others require quantum resources

Summary

Introduction

Bell’s theorem, a landmark result in the foundations of physics, establishes that quantum mechanics is a non-local theory. For each of these games, any sequence of ideal strategies approaching the optimal winning probability does not have a well-defined limit, and the optimal correlation cannot be attained exactly (not even in infinite dimensions). Given question sets and answer sets X , Y, A, B, a quantum strategy is specified by Hilbert spaces HA and HB, a pure state jψi 2 HA HB, and projective measurements fΠaAx g a on HA, fΠbBy g b on HB, for x 2 X; y 2 Y.

Results

Conclusion