It is shown that every language in PSPACE, or equivalently every language accepted by an unbounded round interactive proof system, has a one-round, two-prover interactive proof with exponentially small error probability. To obtain this result, the correctness of a simple but powerful method for parallelizing two-prover interactive proofs to reduce their error is proved.>

Structure in Complexity Theory Annual ConferenceDec 10, 200218 citations

Introduction to Quantum Interactive Proof Systems

shahab razavi

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arXiv:0707.1136 · Quantum Information Processing

On the Power of Quantum, One Round, Two Prover Interactive Proof Systems

Alex Rapaport, Amnon Ta‐Shma

Published Nov 16, 2007• 3 citations

arXiv HTML PDF

DOI: 10.1007/s11128-007-0068-z

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It is known that there exist multi-prover interactive protocols (

\mathsf{MIP}

protocols) for the complexity class

\mathsf{NEXP}

, succinct

\mathsf{MIP}

protocols for

\mathsf{NP}

and multi-prover interactive protocols with shared entanglement (

\mathsf{MIP}^\ast

protocols) for

\mathsf{RE}

. This extraordinary power of multi-prover interactive proof systems comes from the assumption that provers do not communicate with each other during the protocols. If they are allowed to communicate freely, the setting is the same as in the single-prover case, and the computational power of the system becomes significantly weaker. In this paper, we investigate for the first time the setting where communication (i.e., leakage of information) between provers is allowed but bounded. We introduce two techniques to approach this question and show that multi-prover interactive proof systems are robust against some amount of leakage. Our first technique is based on parallel repetition theorems. We apply it to show that for any polynomial

p

, we can construct two-prover one-round

\mathsf{MIP}

and

\mathsf{MIP}^\ast

protocols for

\mathsf{NEXP}

and

\mathsf{RE}

, respectively, that are robust against

p(n)

bits of leakage. We further derive our second technique to convert any low-soundness PCP construction to a two-prover one-round

\mathsf{MIP}

protocol for

\mathsf{NP}

robust against leakage. We also discuss the relation between robustness against leakage in multi-prover interactive proof systems and the Sliding Scale Conjecture in the PCP literature.