Analytic Cancellation of Interference Terms and Closed-Form 1-Mode Marginals in Canonical Boson Sampling
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Quantum Physics arXiv:2603.02272 (quant-ph) [Submitted on 1 Mar 2026] Title:Analytic Cancellation of Interference Terms and Closed-Form 1-Mode Marginals in Canonical Boson Sampling Authors:Jiang Liu View a PDF of the paper titled Analytic Cancellation of Interference Terms and Closed-Form 1-Mode Marginals in Canonical Boson Sampling, by Jiang Liu View PDF HTML (experimental) Abstract:Although the $k$-mode marginal distributions of Canonical Boson Sampling (CBS) are known to be computable in polynomial time, the physical mechanism driving this computational efficiency remains mathematically opaque. In this work, we provide a direct, bottom-up physical derivation of the exact 1-mode marginal distribution in CBS, computable in $\mathcal{O}(R^2)$ time, where $R$ is the total number of photons. We explicitly bridge this physical derivation with the mathematical theory of rank-1 matrix permanents, proving that multiphoton interference natively reduces to a symmetric polynomial scaled by a factorial bosonic bunching factor. Crucially, we demonstrate that our recursive combinatorial formulation circumvents the algorithmic overhead of characteristic function methods, entirely bypassing the need for polynomial interpolation or Fourier transforms. Finally, we apply this formula to identify macroscopic signatures of bunching, providing a rigorous, highly scalable metric for distinguishing genuine quantum interference from classical distinguishable-particle models using standard threshold detectors. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.02272 [quant-ph] (or arXiv:2603.02272v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.02272 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jiang Liu [view email] [v1] Sun, 1 Mar 2026 04:26:35 UTC (36 KB) Full-text links: Access Paper: View a PDF of the paper titled Analytic Cancellation of Interference Terms and Closed-Form 1-Mode Marginals in Canonical Boson Sampling, by Jiang LiuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)