Multi-prover interactive proofs: how to remove intractability assumptions
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
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 Review
SIAM Journal on Computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Parallelization, amplification, and exponential time simulation of quantum interactive proof systems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
PSPACE Has Constant-Round Quantum Interactive Proof Systems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Quantum multi-prover interactive proof systems with limited prior entanglement
Journal of Computer and System Sciences
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Consequences and Limits of Nonlocal Strategies
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Parallel repetition: simplifications and the no-signaling case
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Understanding Parallel Repetition Requires Understanding Foams
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Entanglement in interactive proof systems with binary answers
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
Parallel repetition of entangled games
Proceedings of the forty-third annual ACM symposium on Theory of computing
Entangled Games Are Hard to Approximate
SIAM Journal on Computing
QMA variants with polynomially many provers
Quantum Information & Computation
Multipartite entanglement in XOR games
Quantum Information & Computation
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We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier's verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to coordinate their behavior using a shared entangled quantum state, a perfect parallel repetition theorem holds in the following sense. The prover's optimal success probability for simultaneously playing a collection of XOR proof systems is exactly the product of the individual optimal success probabilities. This property is remarkable in view of the fact that, in the classical case (where the provers can only utilize classical information), it does not hold. The theorem is proved by analyzing parities of XOR proof systems using semidefinite programming techniques, which we then relate to parallel repetitions of XOR games via Fourier analysis.