The Link between Entropic Uncertainty and Nonlocality

TL;DR

This paper establishes a quantitative link between the uncertainty principle and nonlocal correlations in quantum physics, providing an entropic uncertainty relation tied to Bell inequality violations with applications in quantum cryptography.

Contribution

It introduces a novel entropic uncertainty relation that relates measurement uncertainty to Bell inequality violations, connecting two fundamental quantum phenomena.

Findings

Uncertainty bound expressed via Bell inequality violation

Application to certifying quantum sources in cryptography

Quantitative relation between nonlocality and measurement uncertainty

Abstract

Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such that their outcomes cannot both be predicted. On the other hand, nonlocal correlations of measurement outcomes at different locations cannot be explained by classical physics, but appear in the presence of entanglement. Here, we show that these two fundamental quantum effects are quantitatively related. Namely, we provide an entropic uncertainty relation for the outcomes of two binary measurements, where the lower bound on the uncertainty is quantified in terms of the maximum Clauser-Horne-Shimony-Holt value that can be achieved with these measurements. We discuss applications of this uncertainty relation in quantum cryptography, in particular, to certify quantum sources using untrusted devices.