Unbounded entanglement in nonlocal games
Abstract
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 $c\geq 0.13$. 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:
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arXiv e-prints
- Pub Date:
- February 2014
- DOI:
- 10.48550/arXiv.1402.4145
- arXiv:
- arXiv:1402.4145
- Bibcode:
- 2014arXiv1402.4145M
- Keywords:
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- Quantum Physics
- E-Print:
- We have removed the inaccurate discussion of infinite-dimensional strategies in Section 5. Other minor corrections