Multiplayer parallel repetition without dependency-breaking and anchoring variables: monotonic, concave amplification
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Quantum Physics arXiv:2605.08259 (quant-ph) [Submitted on 7 May 2026] Title:Multiplayer parallel repetition without dependency-breaking and anchoring variables: monotonic, concave amplification Authors:Pete Rigas View a PDF of the paper titled Multiplayer parallel repetition without dependency-breaking and anchoring variables: monotonic, concave amplification, by Pete Rigas View PDF Abstract:We obtain quantitative estimates on the decay of the multiplayer optimal value under parallel repetition. In comparison to a previous work of the author in 2025 (arXiv: 2508.09380) which sought to generalize dependency-breaking and anchoring variables from two-player Quantum games, being able to establish quantitative estimates on the decay of the optimal value of a multiplayer game under parallel repetition is of interest to establish under different assumptions. Specifically, independently of the dependency-breaking and anchoring variables that have previously been employed to remove correlations from entangled information shared between Alice and Bob (hence removing dependencies), monotonic concave functions can be used in place of such variables to obtain rates of decay on the optimal value. The game-theoretic setting with two players was first analyzed with monotonic concave functions by Lanzenberger and Maurer. For $q_i , x_i > 0$ $\forall 1 \leq i \leq N$ where $N > 0 $ is the total number of players we adddress an open question raised in their work regarding potential generalizations of two-player monotonic concave functions, through amplification functions of the form $\Psi_{\textit{Mult}} \equiv \Psi = N - \underset{1 \leq i \leq N}{\prod} \mathrm{exp} \big[ - q_i x_i \big]$, which in the multiplayer game-theoretic setting have more intricate combinatorial structures. Comments: Subjects: Quantum Physics (quant-ph); Probability (math.PR) MSC classes: 81P02, 81Q02 Cite as: arXiv:2605.08259 [quant-ph] (or arXiv:2605.08259v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.08259 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Pete Rigas [view email] [v1] Thu, 7 May 2026 21:57:54 UTC (45 KB) Full-text links: Access Paper: View a PDF of the paper titled Multiplayer parallel repetition without dependency-breaking and anchoring variables: monotonic, concave amplification, by Pete RigasView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math.PR 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?) 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?)