Bounded round interactive proofs in finite groups
SIAM Journal on Discrete Mathematics
Communication complexity
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Consequences and Limits of Nonlocal Strategies
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
On the advantage over a random assignment
Random Structures & Algorithms
Parallel repetition: simplifications and the no-signaling case
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Lower bounds in communication complexity based on factorization norms
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Lower Bounds for Quantum Communication Complexity
SIAM Journal on Computing
Perfect Parallel Repetition Theorem for Quantum Xor Proof Systems
Computational Complexity
Lower Bounds on Quantum Multiparty Communication Complexity
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Linear Equations Modulo 2 and the $L_1$ Diameter of Convex Bodies
SIAM Journal on Computing
A Probabilistic Inequality with Applications to Threshold Direct-Product Theorems
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Quantum Information & Computation
Near-Optimal and Explicit Bell Inequality Violations
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
The Grothendieck Constant is Strictly Smaller than Krivine's Bound
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Bell violations through independent bases games
Quantum Information & Computation
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We study multipartite entanglement in the context of XOR games. In particular, we study the ratio of the entangled and classical biases, which measure the maximum advantage of a quantum or classical strategy over a uniformly random strategy. For the case of two-player XOR games, Tsirelson proved that this ratio is upper bounded by the celebrated Grothendieck constant. In contrast, Pérez-García et al. proved the existence of entangled states that give quantum players an unbounded advantage over classical players in a three-player XOR game. We show that the multipartite entangled states that are most often seen in today's literature can only lead to a bias that is a constant factor larger than the classical bias. These states include GHZ states, any state local-unitarily equivalent to combinations of GHZ and maximally entangled states shared between different subsets of the players (e.g., stabilizer states), as well as generalizations of GHZ states of the form Σiαi|i〉... |i〉 for arbitrary amplitudes αi. Our results have the following surprising consequence: classical three-player XOR games do not follow an XOR parallel repetition theorem, even a very weak one. Besides this, we discuss implications of our results for communication complexity and hardness of approximation. Our proofs are based on novel applications of extensions of Grothendieck's inequality, due to Blei and Tonge, and Carne, generalizing Tsirelson's use of Grothendieck's inequality to bound the bias of two-player XOR games.