The Link between Uncertainty Relations and Non-Locality

Abstract

Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of non-local correlations. The uncertainty principle states that there exist pairs of non-compatible measurements on quantum systems such that their outcomes cannot be simultaneously predicted by any observer. On the other hand, non-local correlations of measurement outcomes at different locations cannot be explained by classical physics, but appear in quantum mechanics in the presence of entanglement. Here, we show that these two essential properties of quantum mechanics are quantitatively related. Namely, we provide an entropic uncertainty relation that gives a lower bound on the uncertainty of the binary outcomes of two measurements in terms of the maximum Clauser-Horne-Shimony-Holt value that can be achieved using the same measurements. We discuss an application of this uncertainty relation to certify a quantum source using untrusted devices.