Entanglement-resistant two-Prover interactive proof systems and non-adaptive PIRs

We show that every language in $\np$ is recognized by a two-prover interactive proof system with the following properties. The proof system is entanglement-resistant (i.e., its soundness is robust against provers who have prior shared entanglement), it has one round of interaction, the provers' answers are single bits, and the completeness-soundness gap is constant (formally, $\np\subseteq \xmips_{1-\varepsilon,1/2+\varepsilon}\mo[2]$, for any~$\varepsilon$ such that $0 < \varepsilon < 1/4$). Our result is based on the ``oracularizing" property of a particular private information retrieval scheme (PIR), and it suggests that investigating related properties of other PIRs might bear further fruit.