Uncertainty and Nonlocality

The uncertainty principle states that, two non-commutable physical quantities cannot be measured
with perfect accuracy at the same time. The non-locality concept means that, two subsystems can be strongly correlated even if they are distant. It is reasonable to think that, these two notions may be connected. This is the case, as demonstrated in this report [Science 330, 1072 (2010)]:

Two central concepts of quantum mechanics are Heisenberg’s uncertainty principle and a subtle form of nonlocality that Einstein famously called “spooky action at a distance.” These two fundamental features have thus far been distinct concepts. We show that they are inextricably and quantitatively linked: Quantum mechanics cannot be more nonlocal with measurements that respect the uncertainty principle. In fact, the link between uncertainty and nonlocality holds for all physical
theories. More specifically, the degree of nonlocality of any theory is determined by two factors: the strength of the uncertainty principle and the strength of a property called “steering,” which determines which states can be prepared at one location given a measurement at another.