Unbounded entanglement in nonlocal games (pp1317-1332)
          Laura Mančinska and Thomas Vidick
          doi: https://doi.org/10.26421/QIC15.15-16-4
Abstracts: Quantum entanglement is known to provide a strong advantage in many two-party distributed tasks. We investigate the question of how much entanglement is needed to reach optimal performance. For the first time we show that there exists a purely classical scenario for which no finite amount of entanglement suffices. To this end we introduce a simple two-party nonlocal game H, inspired by Lucien Hardy�s paradox. In our game each player has only two possible questions and can provide bit strings of any finite length as answer. We exhibit a sequence of strategies which use entangled states in increasing dimension d and succeed with probability 1 − O(d−c ) for some c ≥ 0.13. On the other hand, we show that any strategy using an entangled state of local dimension d has success probability at most 1 − Ω(d−2 ). In addition, we show that any strategy restricted to producing answers in a set of cardinality at most d has success probability at most 1 − Ω(d−2 ). Finally, we generalize our construction to derive similar results starting from any game G with two questions per player and finite answers sets in which quantum strategies have an advantage.
Key words: nonlocal game, value of the game, entanglement, dimension witness