This paper studies a generalization of multi-prover interactive proofs in which a verifier interacts with two competing teams of provers: one team attempts to convince the verifier to accept while the other attempts to convince the verifier to reject.Each team consists of two provers who jointly implement a no-signaling strategy.No-signaling strategies are a curious class of joint strategy that cannot in general be implemented without communication between the provers, yet cannot be used as a black box to establish communication between them.Attention is restricted in this paper to two-turn interactions in which the verifier asks questions of each of the four provers and decides whether to accept or reject based on their responses.We prove that the complexity class of decision problems that admit two-turn interactive proofs with competing teams of no-signaling provers is a subset of PSPACE.This upper bound matches existing PSPACE lower bounds on the following two disparate and weaker classes of interactive proof:1. Two-turn multi-prover interactive proofs with only one team of no-signaling provers.2. Two-turn competing-prover interactive proofs with only one prover per team.
This paper studies a generalization of multi-prover interactive proofs in which a verifier interacts with two competing teams of provers: one team attempts to convince the verifier to accept while the other attempts to convince the verifier to reject.Each team consists of two provers who jointly implement a no-signaling strategy.No-signaling strategies are a curious class of joint strategy that cannot in general be implemented without communication between the provers, yet cannot be used as a black box to establish communication between them.Attention is restricted in this paper to two-turn interactions in which the verifier asks questions of each of the four provers and decides whether to accept or reject based on their responses.We prove that the complexity class of decision problems that admit two-turn interactive proofs with competing teams of no-signaling provers is a subset of PSPACE.This upper bound matches existing PSPACE lower bounds on the following two disparate and weaker classes of interactive proof:1. Two-turn multi-prover interactive proofs with only one team of no-signaling provers.2. Two-turn competing-prover interactive proofs with only one prover per team.
Abstract. This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that every language having an ordinary quantum interactive proof system also has a quantum refereed game in which the verifier exchanges just one round of messages with each prover. A key part of our proof is the fact that there exists a single quantum measurement that reliably distinguishes between mixed states chosen arbitrarily from disjoint convex sets having large minimal trace distance from one another. We also show how to reduce the probability of error for some classes of quantum refereed games. 1
Single-prover interactive proofs can recognize PSPACE; if certain complexity assumptions are made, they can do so in zero-knowledge. Generalizing to multiple non-communicating provers extends this class to NEXP, and at the same time removes the complexity assumption needed for zero-knowledge. \n \nHowever, it was recently discovered that the non-communication condition might be insufficient to guarantee soundness. The provers can form joint randomness through non-local computation without communicating. This could break protocols that rely on the statistical independence of the provers. \n \nIn this work, we analyze multi-prover interactive proofs under the constraint of statistical isolation which prohibits non-local computation. We show that there exists perfect zero-knowledge proofs for NEXP under statistical isolation.
Non-signaling proofs, motivated by quantum computation, have found applications in cryptography and hardness of approximation. An important open problem is characterizing the power of no-signaling proofs. It is known that 2-prover no-signaling proofs are characterized by PSPACE, and that no-signaling proofs with poly(n)-provers are characterized by EXP. However, the power of k-prover no-signaling proofs, for 2kpoly(n) remained an open problem. We show that k-prover no-signaling proofs (with negligible soundness) for k=O(√logn) are contained in PSPACE. We prove this via two different routes that are of independent interest. In both routes we consider a relaxation of no-signaling called sub-no-signaling. Our main technical contribution (which is used in both our proofs) is a reduction showing how to convert any sub-no-signaling strategy with value at least 1−2−Ω(k2) into a no-signaling one with value at least 2−O(k2). In the first route, we show that the classical prover reduction method for converting k-prover games into 2-prover games carries over to the no-signaling setting with the following loss in soundness: if a k-player game has value less than 2−ck2 (for some constant~c>0), then the corresponding 2-prover game has value at most 1−2dk2 (for some constant~d>0). In the second route we show that the value of a sub-no-signaling game can be approximated in space that is polynomial in the communication complexity and exponential in the number of provers.
It is known that there exist multi-prover interactive protocols (MIP protocols) for the complexity class NEXP, succinct MIP protocols for NP and multi-prover interactive protocols with shared entanglement (MIP∗ protocols) for 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 MIP and MIP∗ protocols for NEXP and 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 MIP protocol for 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.
We show that any number of parties can coherently exchange any one pure quantum state for another, without communication, given prior shared entanglement. Two applications of this fact to the study of multi-prover quantum interactive proof systems are given. First, we prove that there exists a one-round two-prover quantum interactive proof system for which no finite amount of shared entanglement allows the provers to implement an optimal strategy. More specifically, for every fixed input string, there exists a sequence of strategies for the provers, with each strategy requiring more entanglement than the last, for which the probability for the provers to convince the verifier to accept approaches 1. It is not possible, however, for the provers to convince the verifier to accept with certainty with a finite amount of shared entanglement. The second application is a simple proof that multi-prover quantum interactive proofs can be transformed to have near-perfect completeness by the addition of one round of communication.
We construct a 1-round delegation scheme (i.e., argument-system) for every language computable in time t = t ( n ), where the running time of the prover is poly ( t ) and the running time of the verifier is n · polylog ( t ). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. Our construction relies on the existence of a computational sub-exponentially secure private information retrieval ( PIR ) scheme. The proof exploits a curious connection between the problem of computation delegation and the model of multi-prover interactive proofs that are sound against no-signaling (cheating) strategies , a model that was studied in the context of multi-prover interactive proofs with provers that share quantum entanglement, and is motivated by the physical principle that information cannot travel faster than light. For any language computable in time t = t ( n ), we construct a multi-prover interactive proof ( MIP ), that is, sound against no-signaling strategies, where the running time of the provers is poly ( t ), the number of provers is polylog ( t ), and the running time of the verifier is n · polylog ( t ). In particular, this shows that the class of languages that have polynomial-time MIP s that are sound against no-signaling strategies, is exactly EXP . Previously, this class was only known to contain PSPACE . To convert our MIP into a 1-round delegation scheme, we use the method suggested by Aiello et al. (ICALP, 2000), which makes use of a PIR scheme. This method lacked a proof of security. We prove that this method is secure assuming the underlying MIP is secure against no-signaling provers.