A physical theory is called non-local when observers can produce instantaneous effects over distant systems. Non-local theories rely on two fundamental effects: local uncertainty relations and steering of physical states at a distance. In quantum mec
hanics, the former one dominates the other in a well-known class of non-local games known as XOR games. In particular, optimal quantum strategies for XOR games are completely determined by the uncertainty principle alone. This breakthrough result has yielded the fundamental open question whether optimal quantum strategies are always restricted by local uncertainty principles, with entanglement-based steering playing no role. In this work, we provide a negative answer to the question, showing that both steering and uncertainty relations play a fundamental role in determining optimal quantum strategies for non-local games. Our theoretical findings are supported by an experimental implementation with entangled photons.
Pure states are very important in any theory since they represent states of maximal information about the system within the theory. Here, we show that no non-trivial (not local realistic) extremal states (boxes) of general no-signaling theories can b
e realized within quantum theory. We then explore three interesting consequences of this fact. Firstly, since the pure states are uncorrelated from the environment, the statement forms a no-go result against the most straightforward device-independent protocol for randomness or secure key generation against general no-signaling adversaries. It also leads to the interesting question whether all non-extremal boxes allow for non-local correlations with the adversary. Secondly, in addition to the fact that new information-theoretic principles (designed to pick out the set of quantum correlations from among all non signaling ones) can in consequence be tested on arbitrary non-local vertices to check their validity, it also allows the possibility of excluding from the quantum set any box of no-signaling correlations that can be distilled to a non-local vertex. Finally, it also forms a sufficient condition to identify non-local games with no quantum winning strategy, when one can show that the game has a single unique non-signaling winning strategy. We illustrate each of these consequences with the example of generalized Popescu-Rohrlich boxes.
