Non-Locality in Interactive Proofs

In multi-prover interactive proofs (MIPs), the verifier is usually non-adaptive. This stems from an implicit problem which we call ``contamination'' by the verifier. We make explicit the verifier contamination problem, and identify a solution by constructing a generalization of the MIP model. This new model quantifies non-locality as a new dimension in the characterization of MIPs. A new property of zero-knowledge emerges naturally as a result by also quantifying the non-locality of the simulator.Comment: 32 pages, 14 figures. Submitted to Crypto 2019, Feb 2019. Report arXiv:1804.02724 merged here in the update proces

Perfect zero knowledge for quantum multiprover interactive proofs

In this work we consider the interplay between multiprover interactive proofs, quantum entanglement, and zero knowledge proofs - notions that are central pillars of complexity theory, quantum information and cryptography. In particular, we study the relationship between the complexity class MIP$^*$, the set of languages decidable by multiprover interactive proofs with quantumly entangled provers, and the class PZKMIP$^*$, which is the set of languages decidable by MIP$^*$ protocols that furthermore possess the perfect zero knowledge property. Our main result is that the two classes are equal, i.e., MIP$^* =$ PZKMIP$^*$. This result provides a quantum analogue of the celebrated result of Ben-Or, Goldwasser, Kilian, and Wigderson (STOC 1988) who show that MIP $=$ PZKMIP (in other words, all classical multiprover interactive protocols can be made zero knowledge). We prove our result by showing that every MIP$^*$ protocol can be efficiently transformed into an equivalent zero knowledge MIP$^*$ protocol in a manner that preserves the completeness-soundness gap. Combining our transformation with previous results by Slofstra (Forum of Mathematics, Pi 2019) and Fitzsimons, Ji, Vidick and Yuen (STOC 2019), we obtain the corollary that all co-recursively enumerable languages (which include undecidable problems as well as all decidable problems) have zero knowledge MIP$^*$ protocols with vanishing promise gap