Two-prover one-round proof systems: their power and their problems (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On the power of multi-prover interactive protocols
Theoretical Computer Science
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Two-Prover Protocols---Low Error at Affordable Rates
SIAM Journal on Computing
Consequences and Limits of Nonlocal Strategies
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Understanding Parallel Repetition Requires Understanding Foams
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Assignment Testers: Towards a Combinatorial Proof of the PCP Theorem
SIAM Journal on Computing
Parallel repetition in projection games and a concentration bound
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Unique games on expanding constraint graphs are easy: extended abstract
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Uniform direct product theorems: simplified, optimized, and derandomized
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Perfect Parallel Repetition Theorem for Quantum Xor Proof Systems
Computational Complexity
Entangled Games are Hard to Approximate
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Unique Games with Entangled Provers are Easy
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Locally Testing Direct Product in the Low Error Range
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
A Counterexample to Strong Parallel Repetition
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Rounding Parallel Repetitions of Unique Games
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
New direct-product testers and 2-query PCPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Oracularization and Two-Prover One-Round Interactive Proofs against Nonlocal Strategies
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Strong Parallel Repetition Theorem for Free Projection Games
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
No Strong Parallel Repetition with Entangled and Non-signaling Provers
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Derandomized Parallel Repetition of Structured PCPs
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
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We consider one-round games between a classical referee and two players. One of the main questions in this area is the parallel repetition question: Is there a way to decrease the maximum winning probability of a game without increasing the number of rounds or the number of players? Classically, efforts to resolve this question, open for many years, have culminated in Raz's celebrated parallel repetition theorem on one hand, and in efficient product testers for PCPs on the other. In the case where players share entanglement, the only previously known results are for special cases of games, and are based on techniques that seem inherently limited. Here we show for the first time that the maximum success probability of entangled games can be reduced through parallel repetition, provided it was not initially 1. Our proof is inspired by a seminal result of Feige and Kilian in the context of classical two-prover one-round interactive proofs. One of the main components in our proof is an orthogonalization lemma for operators, which might be of independent interest.