Passive-User Bell-State Loop-Back Key Establishment without Quantum Detectors at the User Nodes

Quantum Physics [Submitted on 17 Jun 2026] Passive-User Bell-State Loop-Back Key Establishment without Quantum Detectors at the User Nodes Luis Adrián Lizama-Pérez 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 Submission history From: Luis Adrián Lizama-Pérez [view email] [v1] Wed, 17 Jun 2026 19:49:17 UTC (17 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-06 Change to browse by: cs cs.CR References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)