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Related papers: On quantum interactive proofs with short messages

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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

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…

Computational Complexity · Computer Science 2013-08-08 Gus Gutoski

We identify a formal connection between physical problems related to the detection of separable (unentangled) quantum states and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum…

Quantum Physics · Physics 2015-03-27 Gus Gutoski , Patrick Hayden , Kevin Milner , Mark M. Wilde

In this article we introduce a new complexity class called PQMA_log(2). Informally, this is the class of languages for which membership has a logarithmic-size quantum proof with perfect completeness and soundness which is polynomially close…

Quantum Physics · Physics 2016-11-25 Hugue Blier , Alain Tapp

We present a classical interactive protocol that verifies the validity of a quantum witness state for the local Hamiltonian problem. It follows from this protocol that approximating the non-local value of a multi-player one-round game to…

Quantum Physics · Physics 2015-05-28 Zhengfeng Ji

In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an (information-theoretically secure) streaming proof with a…

Quantum Physics · Physics 2023-07-21 Uma Girish , Ran Raz , Wei Zhan

This paper studies multiple-proof quantum Merlin-Arthur (QMA) proof systems in the setting when the completeness-soundness gap is small. Small means that we only lower-bound the gap with an inverse-exponential function of the input length,…

Quantum Physics · Physics 2012-05-15 Attila Pereszlényi

We show how to encode $2^n$ (classical) bits $a_1,...,a_{2^n}$ by a single quantum state $|\Psi>$ of size O(n) qubits, such that: for any constant $k$ and any $i_1,...,i_k \in \{1,...,2^n\}$, the values of the bits $a_{i_1},...,a_{i_k}$ can…

Quantum Physics · Physics 2007-05-23 Ran Raz

In this paper we explore the power of AM for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA)--introduced by Ambainis and Watrous in 2002--and the communications are classical. It is of…

Computational Complexity · Computer Science 2015-05-05 Shenggen Zheng , Daowen Qiu , Jozef Gruska

We propose a monotonic logic of internalised non-monotonic or instant interactive proofs (LiiP) and reconstruct an existing monotonic logic of internalised monotonic or persistent interactive proofs (LiP) as a minimal conservative extension…

Logic in Computer Science · Computer Science 2013-02-07 Simon Kramer

We consider the recursive Fourier sampling problem (RFS), and show that there exists an interactive proof for RFS with an efficient classical verifier and efficient quantum prover.

Quantum Physics · Physics 2011-08-25 Matthew McKague

We show several results related to interactive proof modes of communication complexity. First we show lower bounds for the QMA-communication complexity of the functions Inner Product and Disjointness. We describe a general method to prove…

Computational Complexity · Computer Science 2011-01-04 Hartmut Klauck

We explore quantum-inspired interactive proof systems where the prover is limited. Namely, we improve on a result by [AG17] showing a quantum-inspired interactive protocol ($\sf IP$) for $\sf PreciseBQP$ where the prover is only assumed to…

Quantum Physics · Physics 2021-11-08 Ayal Green , Guy Kindler , Yupan Liu

The round complexity of interactive proof systems is a key question of practical and theoretical relevance in complexity theory and cryptography. Moreover, results such as QIP = QIP(3) (STOC'00) show that quantum resources significantly…

Quantum Physics · Physics 2024-05-29 Alex B. Grilo , Philippe Lamontagne

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

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

It is known that there exist multi-prover interactive protocols ($\mathsf{MIP}$ protocols) for the complexity class $\mathsf{NEXP}$, succinct $\mathsf{MIP}$ protocols for $\mathsf{NP}$ and multi-prover interactive protocols with shared…

Quantum Physics · Physics 2026-05-19 Vahid R. Asadi , Atsuya Hasegawa , François Le Gall

We construct a classically verifiable succinct interactive argument for quantum computation (BQP) with communication complexity and verifier runtime that are poly-logarithmic in the runtime of the BQP computation (and polynomial in the…

In recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine.…

Quantum Physics · Physics 2021-02-12 Federico Centrone , Niraj Kumar , Eleni Diamanti , Iordanis Kerenidis

QMA (Quantum Merlin Arthur) is the class of problems which, though potentially hard to solve, have a quantum solution which can be verified efficiently using a quantum computer. It thus forms a natural quantum version of the classical…

Quantum Physics · Physics 2016-03-02 Tomoyuki Morimae , Daniel Nagaj , Norbert Schuch