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We present a protocol that transforms any quantum multi-prover interactive proof into a nonlocal game in which questions consist of logarithmic number of bits and answers of constant number of bits. As a corollary, this proves that the…

Quantum Physics · Physics 2016-10-12 Zhengfeng Ji

We show that, for any language in NP, there is an entanglement-resistant constant-bit two-prover interactive proof system with a constant completeness vs. soundness gap. The previously proposed classical two-prover constant-bit interactive…

Quantum Physics · Physics 2007-07-13 Richard Cleve , Dmitry Gavinsky , Rahul Jain

Multi Prover Interactive Proof systems (MIPs)were first presented in a cryptographic context, but ever since they were used in various fields. Understanding the power of MIPs in the quantum context raises many open problems, as there are…

Quantum Physics · Physics 2008-06-26 Michael Ben-Or , Avinatan Hassidim , Haran Pilpel

We show that if a language $L$ admits a public-coin unambiguous interactive proof (UIP) with round complexity $\ell$, where $a$ bits are communicated per round, then the batch language $L^{\otimes k}$, i.e. the set of $k$-tuples of…

Computational Complexity · Computer Science 2025-10-23 Bonnie Berger , Rohan Goyal , Matthew M. Hong , Yael Tauman Kalai

Following an early work of Dwork and Stockmeyer on interactive proof systems whose verifiers are two-way probabilistic finite automata, the authors initiated in 2004 a study on the computational power of quantum interactive proof systems…

Quantum Physics · Physics 2015-08-25 Harumichi Nishimura , Tomoyuki Yamakami

A central problem in quantum computational complexity is how to prevent entanglement-assisted cheating in multi-prover interactive proof systems. It is well-known that the standard oracularization technique completely fails in some proof…

Quantum Physics · Physics 2008-10-06 Tsuyoshi Ito , Hirotada Kobayashi , Keiji Matsumoto

$\text{MIP}^\ast$ is the class of languages decidable by an efficient classical verifier interacting with multiple quantum provers that share entangled qubits but cannot communicate. Notably, $\text{MIP}^\ast$ was proved to equal…

Quantum Physics · Physics 2025-09-04 Itay Shalit

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…

Quantum Physics · Physics 2019-05-28 Alex B. Grilo , William Slofstra , Henry Yuen

This paper presents stronger methods of achieving perfect completeness in quantum interactive proofs. First, it is proved that any problem in QMA has a two-message quantum interactive proof system of perfect completeness with constant…

Quantum Physics · Physics 2016-05-25 Hirotada Kobayashi , François Le Gall , Harumichi Nishimura

Whereas quantum complexity theory has traditionally been concerned with problems arising from classical complexity theory (such as computing boolean functions), it also makes sense to study the complexity of inherently quantum operations…

Quantum Physics · Physics 2021-11-12 Gregory Rosenthal , Henry Yuen

The widely held belief that BQP strictly contains BPP raises fundamental questions: if we cannot efficiently compute predictions for the behavior of quantum systems, how can we test their behavior? In other words, is quantum mechanics…

Quantum Physics · Physics 2017-04-17 Dorit Aharonov , Michael Ben-Or , Elad Eban , Urmila Mahadev

The central question in quantum multi-prover interactive proof systems is whether or not entanglement shared between provers affects the verification power of the proof system. We study for the first time positive aspects of prior…

Quantum Physics · Physics 2007-11-26 Julia Kempe , Hirotada Kobayashi , Keiji Matsumoto , Thomas Vidick

We present three protocols for verifying all languages: (i) For any unary (binary) language, there is a log-space (linear-space) interactive proof system (IPS); (ii) for any language, there is a constant-space weak-IPS (the non-members may…

Computational Complexity · Computer Science 2018-07-13 Maksims Dimitrijevs , Abuzer Yakaryılmaz

$ \newcommand{\Xlin}{\mathcal{X}} \newcommand{\Zlin}{\mathcal{Z}} \newcommand{\C}{\mathbb{C}} $We give a quantum multiprover interactive proof system for the local Hamiltonian problem in which there is a constant number of provers,…

Quantum Physics · Physics 2015-12-08 Anand Natarajan , Thomas Vidick

We analyze quantum two prover one round interactive proof systems, in which noninteracting provers can share unlimited entanglement. The maximum acceptance probability is characterized as a superoperator norm. We get some partial results…

Quantum Physics · Physics 2007-07-10 Alex Rapaport , Amnon Ta-Shma

Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…

Logic in Computer Science · Computer Science 2014-05-15 Thomas Gransden , Neil Walkinshaw , Rajeev Raman

Interactive proof systems whose verifiers are constant-space machines have interesting features that do not have counterparts in the better studied case where the verifiers operate under reasonably large space bounds. The language…

Computational Complexity · Computer Science 2025-12-17 M. Utkan Gezer , A. C. Cem Say

We show a general method of compiling any $k$-prover non-local game into a single-prover interactive game maintaining the same (quantum) completeness and (classical) soundness guarantees (up to negligible additive factors in a security…

Quantum Physics · Physics 2022-03-31 Yael Kalai , Alex Lombardi , Vinod Vaikuntanathan , Lisa Yang

Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…

Quantum Physics · Physics 2016-10-07 Thomas Vidick , John Watrous

Condon and Lipton (FOCS 1989) showed that the class of languages having a space-bounded interactive proof system (IPS) is a proper subset of decidable languages, where the verifier is a probabilistic Turing machine. In this paper, we show…

Computational Complexity · Computer Science 2012-07-18 Abuzer Yakaryilmaz