Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1910.02590

Non-Signaling Proofs with $O(\sqrt{\log n})$ Provers are in PSPACE

Dhiraj Holden, Yael Tauman Kalai

Published Oct 7, 2019• 0 citations
arXivHTMLPDF

Abstract

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 $20$), then the corresponding 2-prover game has value at most $1 - 2^{dk^2}$ (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.

DOI
10.48550/arxiv.1910.02590

Related papers

Non-signaling proofs with o(√ log n) provers are in PSPACE

Dhiraj Holden, Yael Tauman Kalai

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 non-signaling proofs. It is known that non-signaling proofs with two provers are characterized by PSPACE and that non-signaling proofs with poly(n)-provers are characterized by EXP. However, the power of k-prover non-signaling proofs, for 2<k<(n) remained an open problem.

ACM Symposium on Theory of Computing (STOC)•Jun 7, 2020•1 citation

Non-Signaling Proofs with O(√log n) Provers is in PSPACE

Dhiraj Holden, Yael Tauman Kalai

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.

•Jun 1, 2020•0 citations

How to Delegate Computations: The Power of No-Signaling Proofs

Yael Tauman Kalai, Ran Raz, Ron D. Rothblum

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.

Journal of the ACM•Nov 29, 2021•16 citations

On the Power of Entangled Provers: Immunizing games against entanglement

Julia Kempe, Hirotada Kobayashi, Keiji Matsumoto +2 more

We describe two generic ways to make multi-prover classical games resistant against entangled provers. The first uses quantum communication and a quantum verifier, the second adds an additional prover. This leads to several new results on the power of proof systems with entangled provers. We show that NEXP ⊆ QMIP1,s(2, 1) and NEXP ⊆ MIP1,s(3, 1) with soundness s = 1− 2− poly(n) and PSPACE ⊆ MIP1,s(2, 1) with soundness s = 1 − 1/ poly(n), providing the first non-trivial bounds in this setting. Moreover, our results imply that, unless P = NP, the value of entangled prover games cannot be computed by semi-definite programs that are polynomial in the size of the verifier’s system, a method that has been successful for more restricted quantum games. ∗also at CNRS & LRI, Univerite de Paris-Sud, Orsay, France †Partially supported by the European Commission under the Integrated Project Qubit Applications (QAP) funded by the IST directorate as Contract Number 015848 and by an Alon Fellowship of the Israeli Higher Council of Academic Research. ‡Part of this work was completed at Caltech. Supported by the National Science Foundation under Grants PHY-0456720 and CCF-0524828, by EU project QAP, and by NWO VICI project 639-023-302. Part of this research has been funded by the Dutch BSIK/BRICKS project. §Work partly done while at LRI, Univ. de Paris-Sud, Orsay.

•Apr 23, 2007•10 citations

Interactive proofs with competing teams of no-signaling provers

Gus Gutoski

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.

arXiv:1012.0821•Chicago Journal of Theoretical Computer Science•Jan 1, 2013•0 citations

PSPACE has 2-round quantum interactive proof systems

John Watrous

In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a quantum interactive proof system that requires only two rounds of communication between the prover and verifier, while having exponentially small (one-sided) probability of error. It follows that quantum interactive proof systems are strictly more powerful than classical interactive proof systems in the constant-round case unless the polynomial time hierarchy collapses to the second level.

arXiv:cs/9901015•Jan 27, 1999•6 citations
Non-Signaling Proofs with O(log⁡n)O(\sqrt{\log n})O(logn​) Provers are in PSPACE
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)poly(n)poly(n)-provers are characterized by EXP. However, the power of kkk-prover no-signaling proofs, for 202020), then the corresponding 2-prover game has value at most 1−2dk21 - 2^{dk^2}1−2dk2 (for some constant~d>0d>0d>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.
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.
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.
We describe two generic ways to make multi-prover classical games resistant against entangled provers. The first uses quantum communication and a quantum verifier, the second adds an additional prover. This leads to several new results on the power of proof systems with entangled provers. We show that NEXP ⊆ QMIP1,s(2, 1) and NEXP ⊆ MIP1,s(3, 1) with soundness s = 1− 2− poly(n) and PSPACE ⊆ MIP1,s(2, 1) with soundness s = 1 − 1/ poly(n), providing the first non-trivial bounds in this setting. Moreover, our results imply that, unless P = NP, the value of entangled prover games cannot be computed by semi-definite programs that are polynomial in the size of the verifier’s system, a method that has been successful for more restricted quantum games. ∗also at CNRS & LRI, Univerite de Paris-Sud, Orsay, France †Partially supported by the European Commission under the Integrated Project Qubit Applications (QAP) funded by the IST directorate as Contract Number 015848 and by an Alon Fellowship of the Israeli Higher Council of Academic Research. ‡Part of this work was completed at Caltech. Supported by the National Science Foundation under Grants PHY-0456720 and CCF-0524828, by EU project QAP, and by NWO VICI project 639-023-302. Part of this research has been funded by the Dutch BSIK/BRICKS project. §Work partly done while at LRI, Univ. de Paris-Sud, Orsay.
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.
In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a quantum interactive proof system that requires only two rounds of communication between the prover and verifier, while having exponentially small (one-sided) probability of error. It follows that quantum interactive proof systems are strictly more powerful than classical interactive proof systems in the constant-round case unless the polynomial time hierarchy collapses to the second level.