Andrea Coladangelo, Caltech
In a non-local game, two or more non-communicating, but entangled, players cooperatively try to win a game consisting of a one-round interaction with a classical referee. In this talk, I will describe a two-player non-local game with the property that an epsilon-close to optimal strategy requires the players to share an entangled state of dimension 2^{1/poly(epsilon)}.In particular, a successful strategy in this game requires the two players to be able to "embezzle" an EPR pair into a product state, a task that is known to be impossible to perform exactly, and that requires an exponentially increasing amount of entanglement to perform to increasing precision. This is the best known tradeoff between optimality and dimension. What stands out about our game, though, is that it is surprisingly simple. The design of such a non-local game is inspired by a previous work of Ji, Leung and Vidick, and by techniques from device-independent self-testing. As a corollary, our game provides an alternative proof of the non-closure of the set of quantum correlations.