Polynomial-space approximation of no-signaling provers
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Unique Games with Entangled Provers Are Easy
SIAM Journal on Computing
Parallel repetition of entangled games
Proceedings of the forty-third annual ACM symposium on Theory of computing
A lower bound on the value of entangled binary games
Quantum Information & Computation
Entangled Games Are Hard to Approximate
SIAM Journal on Computing
Quantum interactive proofs with weak error bounds
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization
Journal of the ACM (JACM)
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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This paper presents three results on the power of two-prover one-round interactive proof systems based on oracularization under the existence of prior entanglement between dishonest provers. It is proved that the two-prover one-round interactive proof system for PSPACE by Cai, Condon, and Lipton [JCSS 48:183-193, 1994] still achieves exponentially small soundness error in the existence of prior entanglement between dishonest provers (and more strongly, even if dishonest provers are allowed to use arbitrary no-signaling strategies). It follows that, unless the polynomial-time hierarchy collapses to the second level, two-prover systems are still advantageous to single-prover systems even when only malicious provers can use quantum information. It is also shown that a "dummy" question may be helpful when constructing an entanglement-resistant multi-prover system via oracularization. This affirmatively settles a question posed by Kempe et al. [FOCS 2008, pp. 447-456] and every language in NEXP is proved to have a two-prover one-round interactive proof system even against entangled provers, albeit with exponentially small gap between completeness and soundness. In other words, it is NP-hard to approximate within an inverse-polynomial the value of a classical two-prover one-round game against entangled provers. Finally, both for the above proof system for NEXP and for the quantum two-prover one-round proof system for NEXP proposed by Kempe et al., it is proved that exponentially small completeness-soundness gaps are best achievable unless soundness analysis uses the structure of the underlying system with unentangled provers.