A simple two-player dimension witness based on embezzlement

This talk is about certifying high-dimensional entanglement in the setting of non-local games. 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 strikingly simple two-player non-local game with the property that an epsilon-close to optimal strategy requires the two 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. The design of such a non-local game is inspired by techniques from device-independent self-testing. As a corollary, our game provides a new and (arguably) elementary proof of the non-closure of the set of quantum correlations, a celebrated recent result in quantum information theory. Previous proofs employed representation theoretic machinery for finitely-presented groups and C^* algebras.