Computability limits nonlocal correlations

Abstract

If the no-signaling principle was the only limit to the strength of nonlocal correlations, we would expect that any form of no-signaling correlation can indeed be realized. That is, there exists a state and measurements that remote parties can implement to obtain any such correlation. Here, we show that in any theory in which some functions cannot be computed, there must be further limits to nonlocal correlations than the no-signaling principle alone. We proceed to argue that even in a theory such as quantum mechanics in which nonlocal correlations are already weaker, the question of computability imposes such limits. © 2012 American Physical Society.