Unbounded entanglement in nonlocal games
Abstract
Quantum entanglement is known to provide a strong advantage in many twoparty 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 twoparty 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 $1O(d^{c})$ for some $c\geq 0.13$. On the other hand, we show that any strategy using an entangled state of local dimension $d$ has success probability at most $1\Omega(d^{2})$. In addition, we show that any strategy restricted to producing answers in a set of cardinality at most $d$ has success probability at most $1\Omega(d^{2})$. 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.4145
 Bibcode:
 2014arXiv1402.4145M
 Keywords:

 Quantum Physics
 EPrint:
 We have removed the inaccurate discussion of infinitedimensional strategies in Section 5. Other minor corrections