An Effective Pauli-Channel Model for Passive-User Loop-Back QKD
Abstract
This work develops an effective channel model for distributed passive-user Loop-Back quantum key distribution. In the intended key-establishment setting, the two passive users B1 and B2 are the legitimate lightweight parties that establish a shared secret key by using Alice as an active quantum preparation-and-measurement infrastructure. A single active station prepares and measures BB84 states, while two remote users apply only local polarization rotations. We show that the passive-user pair can be externally encapsulated as an effective Loop-Back node whose observable action is a balanced mixture of conjugate-basis dephasings, equivalently represented as an anisotropic Pauli channel with identity, X, and Z components and no Y component. This structure differs from isotropic depolarization and recovers the ideal conclusive-event probability Pconc=1/4. The model also clarifies why non-orthogonal intermediate states are necessary for passive-user security. This channel-level description characterizes Alice's observable statistics and provides a compact basis for subsequent analysis of passive-user Loop-Back QKD under realistic optical and adversarial conditions.
Versions
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BibTeX
@misc{lizamaperez2026effective,
title = {{An Effective Pauli-Channel Model for Passive-User Loop-Back QKD}},
author = {Luis Adrián Lizama-Pérez},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.04247},
eprint = {2606.04247},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.04247},
}
RIS
TY - UNPB
TI - An Effective Pauli-Channel Model for Passive-User Loop-Back QKD
AU - Luis Adrián Lizama-Pérez
PY - 2026
DA - 2026/06/02
PB - arXiv
DO - 10.48550/arxiv.2606.04247
UR - https://arxiv.org/abs/2606.04247
AB - This work develops an effective channel model for distributed passive-user Loop-Back quantum key distribution. In the intended key-establishment setting, the two passive users B_1 and B_2 are the legitimate lightweight parties that establish a shared secret key by using Alice as an active quantum preparation-and-measurement infrastructure. A single active station prepares and measures BB84 states, while two remote users apply only local polarization rotations. We show that the passive-user pair can be externally encapsulated as an effective Loop-Back node whose observable action is a balanced mixture of conjugate-basis dephasings, equivalently represented as an anisotropic Pauli channel with identity, X, and Z components and no Y component. This structure differs from isotropic depolarization and recovers the ideal conclusive-event probability P_conc=1/4. The model also clarifies why non-orthogonal intermediate states are necessary for passive-user security. This channel-level description characterizes Alice's observable statistics and provides a compact basis for subsequent analysis of passive-user Loop-Back QKD under realistic optical and adversarial conditions.
ER -