An Effective Pauli-Channel Model for Passive-User Loop-Back QKD
2026-06-02 • Information Theory
Information Theory
AI summaryⓘ
The authors present a simplified model to understand how two users can share a secret key in a quantum communication setup where only one active station, called Alice, sends and measures quantum states, while the other two users only adjust the polarization locally. They describe the combined effect of these users as a special type of quantum channel that mixes certain types of errors but not others, different from common depolarizing noise. Their model explains why certain non-orthogonal quantum states are important for security and matches the expected success rate of key sharing. This helps in analyzing how the system behaves under real-world conditions and potential attacks.
Quantum key distributionBB84 protocolPassive usersPolarization rotationAnisotropic Pauli channelDepolarizationQuantum channel modelConclusive-event probabilityNon-orthogonal statesQuantum security
Authors
Luis Adrián Lizama-Pérez
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 \(B_1\) 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 \(P_{\mathrm{conc}}=1/4\). 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.