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We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive…

Quantum Physics · Physics 2018-06-25 Anne Broadbent

We examine the power of statistical zero knowledge proofs (captured by the complexity class SZK) and their variants. First, we give the strongest known relativized evidence that SZK contains hard problems, by exhibiting an oracle relative…

Computational Complexity · Computer Science 2017-05-10 Adam Bouland , Lijie Chen , Dhiraj Holden , Justin Thaler , Prashant Nalini Vasudevan

Zero-knowledge proofs are mathematical cryptographic methods to demonstrate the validity of a claim while providing no further information beyond the claim itself. The possibility of using such proofs to process classified and other…

Instrumentation and Detectors · Physics 2016-12-02 Sébastien Philippe , Robert J. Goldston , Alexander Glaser , Francesco d'Errico

In this paper we propose a definition for (honest verifier) quantum statistical zero-knowledge interactive proof systems and study the resulting complexity class, which we denote QSZK. We prove several facts regarding this class that…

Quantum Physics · Physics 2007-05-23 John Watrous

Machine learning is increasingly deployed through outsourced and cloud-based pipelines, which improve accessibility but also raise concerns about computational integrity, data privacy, and model confidentiality. Zero-knowledge proofs (ZKPs)…

Cryptography and Security · Computer Science 2026-03-31 Zhizhi Peng , Chonghe Zhao , Taotao Wang , Guofu Liao , Zibin Lin , Yifeng Liu , Bin Cao , Long Shi , Qing Yang , Shengli Zhang

We investigate two resources whose effects on quantum interactive proofs remain poorly understood: the promise of unentanglement, and the verifier's ability to condition on an intermediate measurement, which we call post-measurement…

Quantum Physics · Physics 2025-09-22 Sabee Grewal , William Kretschmer

Uncertainty quantification (UQ) for open-ended language generation remains a critical yet underexplored challenge, especially under black-box constraints where internal model signals are inaccessible. In this paper, we introduce…

Computation and Language · Computer Science 2025-09-08 Beining Xu , Yongming Lu

In this work we consider the following problem: in a Multi-Prover environment, how close can we get to prove the validity of an NP statement in Zero-Knowledge ? We exhibit a set of two novel Zero-Knowledge protocols for the 3-COLorability…

Quantum Physics · Physics 2019-12-20 Claude Crépeau , Arnaud Massenet , Louis Salvail , Lucas Stinchcombe , Nan Yang

Privacy concerns in machine learning systems have grown significantly with the increasing reliance on sensitive user data for training large-scale models. This paper introduces a novel framework combining Probably Approximately Correct…

Cryptography and Security · Computer Science 2026-02-13 Guilhem Repetto , Nojan Sheybani , Gabrielle De Micheli , Farinaz Koushanfar

Low degree tests play an important role in classical complexity theory, serving as basic ingredients in foundational results such as $\mathsf{MIP} = \mathsf{NEXP}$ [BFL91] and the PCP theorem [AS98,ALM+98]. Over the last ten years, versions…

Quantum Physics · Physics 2020-11-21 Zhengfeng Ji , Anand Natarajan , Thomas Vidick , John Wright , Henry Yuen

We consider a type of zero-knowledge protocols that are of interest for their practical applications within networks like the Internet: efficient zero-knowledge arguments of knowledge that remain secure against concurrent man-in-the-middle…

Cryptography and Security · Computer Science 2007-05-23 Yi Deng , Giovanni Di Crescenzo , Dongdai Lin

We construct a publicly-verifiable non-interactive zero-knowledge argument system for QMA with the following properties. 1. Transparent setup. Our protocol only requires a uniformly random string (URS) setup. The only prior…

Quantum Physics · Physics 2025-11-27 James Bartusek , Ruta Jawale , Justin Raizes , Kabir Tomer

Position verification schemes are interactive protocols where entities prove their physical location to others; this enables interactive proofs for statements of the form "I am at a location $L$." Although secure position verification…

Quantum Physics · Physics 2026-02-17 Uma Girish , Greg Gluch , Shafi Goldwasser , Tal Malkin , Leo Orshansky , Henry Yuen

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…

Quantum Physics · Physics 2011-03-11 Debbie Leung , Ben Toner , John Watrous

Over recent decades, machine learning has significantly advanced network communication, enabling improved decision-making, user behavior analysis, and fault detection. Decentralized approaches, where participants exchange computation…

Machine Learning · Computer Science 2025-04-22 Zhibo Xing , Zijian Zhang , Ziang Zhang , Zhen Li , Meng Li , Jiamou Liu , Zongyang Zhang , Yi Zhao , Qi Sun , Liehuang Zhu , Giovanni Russello

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

A critical step in experimental quantum information processing (QIP) is to implement control of quantum systems protected against decoherence via informational encodings, such as quantum error correcting codes, noiseless subsystems and…

Quantum Physics · Physics 2009-09-13 P. Cappellaro , J. S. Hodges , T. F. Havel , D. G. Cory

In a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. In this work, we show that this same task can in fact be…

Quantum Physics · Physics 2022-02-14 Gorjan Alagic , Andrew M. Childs , Alex B. Grilo , Shih-Han Hung

This paper studies the complexity classes QZK and HVQZK of problems having a quantum computational zero-knowledge proof system and an honest-verifier quantum computational zero-knowledge proof system, respectively. The results proved in…

Quantum Physics · Physics 2007-05-23 Hirotada Kobayashi

A zero-knowledge proximity proof certifies geometric nearness but carries no commitment to an application context. In stateful geo-content systems, where drops can share coordinates, policies evolve, and content has persistent identity,…

Cryptography and Security · Computer Science 2026-04-07 Yoshiyuki Ootani