Nonlocal Games through Communication Complexity and Quantum Cryptography Advance Understanding of Correlations and Enable Unclonable Encryption

Quantum Physics arXiv:2510.09457 (quant-ph) [Submitted on 10 Oct 2025] Title:Nonlocal Games Through Communication Complexity and Quantum Cryptography Authors:Pierre Botteron View a PDF of the paper titled Nonlocal Games Through Communication Complexity and Quantum Cryptography, by Pierre Botteron View PDF Abstract:This thesis explores foundational aspects of quantum information theory and quantum cryptography. First, we investigate quantum correlations in interactive settings, including the CHSH and graph isomorphism games. We aim to distinguish quantum correlations from non-signaling correlations by leveraging the principle of communication complexity. To this end, we employ techniques such as distributed computation, majority-function-based distillation protocols, the algebraic and geometric properties of nonlocal box wirings, and variations of some graph properties such as isomorphism, transitivity, and equitable partitions. This inquiry advances our understanding of non-physical correlations. Second, we address a key open problem in cryptography: the feasibility of unclonable encryption. We aim to construct an encryption scheme that prevents two distant parties from simultaneously obtaining information about a shared encrypted message. We introduce a candidate for unclonable encryption in the plain model, i.e. without assumptions, in working towards an unconditional proof. Our protocol is based on Clifford algebra, utilizing complex Hermitian unitary matrices that anti-commute. For small key sizes, we rigorously prove security using sum-of-squares methods, while for larger key sizes, we provide strong numerical evidence via the NPA hierarchy. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Combinatorics (math.CO) Cite as: arXiv:2510.09457 [quant-ph] (or arXiv:2510.09457v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.09457 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Pierre Botteron [view email] [v1] Fri, 10 Oct 2025 15:07:24 UTC (8,567 KB) Full-text links: Access Paper: View a PDF of the paper titled Nonlocal Games Through Communication Complexity and Quantum Cryptography, by Pierre BotteronView PDF view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: math math-ph math.CO math.MP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)