Passive-User Bell-State Loop-Back Key Establishment without Quantum Detectors at the User Nodes
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Quantum Physics arXiv:2606.19551 (quant-ph) [Submitted on 17 Jun 2026] Title:Passive-User Bell-State Loop-Back Key Establishment without Quantum Detectors at the User Nodes Authors:Luis Adrián Lizama-Pérez View a PDF of the paper titled Passive-User Bell-State Loop-Back Key Establishment without Quantum Detectors at the User Nodes, by Luis Adri\'an Lizama-P\'erez View PDF HTML (experimental) Abstract:We propose and analyze a Bell-state extension of the Loop-Back quantum key distribution architecture for secret-key establishment between two passive users that do not require quantum transmitters or quantum detectors. In the proposed setting, a single active station, Alice, provides the entangled-state infrastructure, retains one qubit of an initially prepared Bell pair, and sends the traveling subsystem through two passive users, denoted by $B_1$ and $B_2$. Each passive user applies a local Pauli operation to the same traveling subsystem, so that the operation observed by Alice is only the effective composition $U_{\mathrm{eff}}=U_2U_1$. After the subsystem returns, Alice performs a Bell-state measurement and, using her private knowledge of the initial Bell state, deterministically identifies the effective Pauli operation. However, the individual factors $U_1$ and $U_2$ remain algebraically hidden from Alice whenever the local choices are uniformly and independently selected. The public effective operation acts as a parity-like constraint: each passive user can infer the operation applied by the other from its own private choice, while the active station learns only the global composition. This construction transfers the essential distributed-transformation mechanism of passive-user Loop-Back QKD to the entangled-state regime. Unlike single-qubit passive-user schemes, whose useful events are intrinsically post-selected, the Bell-state version is limited primarily by the success probability of the Bell-state measurement. We discuss the algebraic structure of the protocol, its interpretation as an infrastructure-assisted mediated key-establishment mechanism, and the physical assumptions required to protect passive Pauli modulators against active injection or Trojan-horse-type attacks. Subjects: Quantum Physics (quant-ph); Cryptography and Security (cs.CR) MSC classes: 81P94, 94A60 Cite as: arXiv:2606.19551 [quant-ph] (or arXiv:2606.19551v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.19551 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Luis Adrián Lizama-Pérez [view email] [v1] Wed, 17 Jun 2026 19:49:17 UTC (17 KB) Full-text links: Access Paper: View a PDF of the paper titled Passive-User Bell-State Loop-Back Key Establishment without Quantum Detectors at the User Nodes, by Luis Adri\'an Lizama-P\'erezView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cs cs.CR 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?)