Generating Dicke State Graphs

Quantum Physics arXiv:2609.22564 (quant-ph) [Submitted on 18 Sep 2026] Title:Generating Dicke State Graphs Authors:Rebekah Herrman View a PDF of the paper titled Generating Dicke State Graphs, by Rebekah Herrman View PDF HTML (experimental) Abstract:Graph theory is a powerful tool in quantum computing, with applications ranging from quantum circuit synthesis and optimization to entanglement mapping. Recent work has shown how one can use edge-colored graphs to model photonic experiments that generate GHZ and W states. However, the latter work also proved that verifying that a graph models a Dicke state experiment is coNP-complete. In this work, we provide families of graphs that generate $|D_{k}^a\rangle \otimes |0\rangle^{\otimes b }$, where $b = |a-2k|$ is the number of spectator modes. The graph setup consists of a doubled complete subgraph on $a$ vertices and a collection of auxiliary vertices. We prove that every coincidence carries exactly $k$ excitations, every weight-$k$ computational basis state on bitstrings of length $a$ is realized, and each of those bitstrings is realized exactly $(n/2)!$ times, where $n = a+b$. Since verifying the Dicke FORALL condition is coNP-complete in general, constructing explicit families that provably generate Dicke states is of interest. Subjects: Quantum Physics (quant-ph); Combinatorics (math.CO) Cite as: arXiv:2609.22564 [quant-ph] (or arXiv:2609.22564v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.22564 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Rebekah Herrman [view email] [v1] Fri, 18 Sep 2026 20:32:01 UTC (39 KB) Full-text links: Access Paper: View a PDF of the paper titled Generating Dicke State Graphs, by Rebekah HerrmanView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: math math.CO 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?)