Rotational Bell-State Loop-Back Key Establishment and Agreement Certification for Passive Users
Abstract
Server-aided Bell-state networks with sequential local encoding are an established approach to mediated key distribution. Against this background, we study a Loop-Back architecture in which two source-free, detector-free users transform the same traveling qubit. Alice privately samples r∈ℤ*22, prepares |βr⟩ over the complete Bell basis, retains one qubit, and uses r as the reference for the returned pair. A deterministic Pauli-composition mode, U*eff=U2U1, serves as a reference to prior serial-unitary protocols. The main extension instead uses the two same-axis settings R(±α) and a reference-versus-complement Bell test. Opposite rotations cancel, whereas equal rotations add, so P(C|disagreement)=0 and P(C|agreement)=sin2(2α). At α=π/8, agreement is certified with probability 1/2, and the overall conclusive-key probability is 1/4 for unbiased choices. The same event supplies one shared raw-key bit. For the Pauli mode, a one-qubit Pauli twirl hides either user's factor from an endpoint mediator that may prepare an arbitrary qubit--ancilla state and choose the final measurement, provided the other Pauli is uniform and the traveler is inaccessible between users. The rotational guarantee is narrower: common-sign privacy holds only for the prescribed Bell source and coarse-grained instrument. A polarization implementation can normalize the private reference to the singlet and use a beam splitter with verified two-photon detection; loss produces a third, discarded outcome. The proposal is theoretical and does not claim composable security or experimental validation.
Versions
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BibTeX
@misc{lizamaperez2026rotational,
title = {{Rotational Bell-State Loop-Back Key Establishment and Agreement Certification for Passive Users}},
author = {Luis Adrián Lizama-Pérez},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.19551},
eprint = {2606.19551},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.19551},
}
RIS
TY - UNPB
TI - Rotational Bell-State Loop-Back Key Establishment and Agreement Certification for Passive Users
AU - Luis Adrián Lizama-Pérez
PY - 2026
DA - 2026/08/19
PB - arXiv
DO - 10.48550/arxiv.2606.19551
UR - https://arxiv.org/abs/2606.19551
AB - Server-aided Bell-state networks with sequential local encoding are an established approach to mediated key distribution. Against this background, we study a Loop-Back architecture in which two source-free, detector-free users transform the same traveling qubit. Alice privately samples r∈ℤ*2^2, prepares |β_r⟩ over the complete Bell basis, retains one qubit, and uses r as the reference for the returned pair. A deterministic Pauli-composition mode, U*eff=U_2U_1, serves as a reference to prior serial-unitary protocols. The main extension instead uses the two same-axis settings R(±α) and a reference-versus-complement Bell test. Opposite rotations cancel, whereas equal rotations add, so P(C|disagreement)=0 and P(C|agreement)=sin^2(2α). At α=π/8, agreement is certified with probability 1/2, and the overall conclusive-key probability is 1/4 for unbiased choices. The same event supplies one shared raw-key bit. For the Pauli mode, a one-qubit Pauli twirl hides either user's factor from an endpoint mediator that may prepare an arbitrary qubit--ancilla state and choose the final measurement, provided the other Pauli is uniform and the traveler is inaccessible between users. The rotational guarantee is narrower: common-sign privacy holds only for the prescribed Bell source and coarse-grained instrument. A polarization implementation can normalize the private reference to the singlet and use a beam splitter with verified two-photon detection; loss produces a third, discarded outcome. The proposal is theoretical and does not claim composable security or experimental validation.
ER -