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.
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.
Abstract This work develops effective channel representations and a composable-security framework for distributed passive-user Loop-Back quantum key distribution (QKD). Alice provides trusted preparation-and-measurement infrastructure at local service points, while two source-free and detector-free users, B1 and B2 , apply independently selected polarization rotations R(±π/8) to the same optical carrier. Two complementary derivations describe the honest operation. Direct averaging over the composed rotations gives the observable Loop-Back map, while an operationally equivalent representation on the Bennett–Brassard 1984 (BB84) preparation-and-measurement data is a balanced mixture of conjugate-basis dephasings, or an anisotropic Pauli channel with identity, X , and Z components and no Y component. Both recover the ideal conclusive-event probability Pconc=1/4 . Security is established without restricting the adversarial action to this effective channel. Eve may implement an arbitrary coherent attack with quantum memory on the single untrusted interface between the two local rotations. In the single-photon sector, a Choi-operator identity yields the exact ideal relation e1,p=3e1,b/2 , together with a low-error robust angular bound e1,p≤κrote1,b . Phase-randomized weak coherent pulses, decoy-state estimation and generalized entropy accumulation then give a finite-key composable bound. A common optical model compares asymptotic and finite-block rates and quantifies their convergence with block size. The analysis also identifies the trusted-interface condition required to exclude loss-assisted operation-discrimination attacks and specifies the hardware assumptions needed for optical implementation.
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.
Bidirectional quantum key distribution (QKD) protocols face persistent challenges related to classical disclosure, confinement of the signal space to predictable subspaces, and limited detectability under substitution or entanglement-swapping attacks. In this work, we present a Bell-state extension of the Loop-Back QKD architecture that improves efficiency and detectability while preserving its defining feature of a simplified, measurement-free remote terminal. The protocol employs entangled Bell states together with deterministic local Pauli encoding at the remote node. A central element is that Alice privately prepares and knows the initial Bell state, which serves as a hidden reference enabling her to interpret the Bell-state transition induced by Bob, while preventing an adversary from reconstructing the encoding without access to this reference. By exploiting both intra- and inter-family Bell transitions, the scheme expands the effective signal space beyond the subspace restrictions of earlier two-way protocols. Alice performs a Bell-state measurement to deterministically infer Bob's operation without any basis sifting. Although the traveling subsystem remains locally maximally mixed, concealing the initial Bell family amplifies disturbance under separable substitution strategies, yielding an intrinsic detection probability of approximately 3/4 per round. From an efficiency perspective, the protocol lifts the intrinsic post-selection limitation of single-qubit Loop-Back schemes: the effective throughput is bounded only by the Bell-state measurement success probability, reaching up to 50% in linear-optical implementations. These features make the proposed scheme particularly suitable for mobile or edge-based QKD scenarios, where passive remote nodes must operate under high loss and limited interaction times.
The Loop-Back Quantum Key Distribution (LB-QKD) protocol establishes a bidirectional architecture in which a single photon travels forth and back through the same optical channel. Unlike conventional one-way schemes such as BB84, Alice performs both state preparation and measurement, while Bob acts as a passive polarization modulator and reflector. This design eliminates detectors at Bob's side, minimizes synchronization requirements, and enables compact, low-power implementations suitable for quantum-mobile and IoT platforms. An extended three-basis configuration {X,Y,Z} is introduced, preserving the simplicity of the two-basis scheme while improving noise tolerance through enhanced orthogonality-based filtering. Analytical modeling shows that the effective protocol error decreases from Eprotocol(2)=e/2 to Eprotocol(3)=e/3, achieving a 33% improvement in noise resilience. Despite its slightly lower sifting efficiency (η=1/6), the total information gain reaches G=0.26 bits per pulse, maintaining post-sifting throughput comparable to BB84. The protocol doubles the tolerable QBER of conventional QKD, sustaining secure operation up to 22% for two bases and approximately 47.58% for three bases. Its passive, self-verifying architecture enhances resistance to man-in-the-middle, photon-number-splitting, and side-channel attacks, providing a scalable and energy-efficient framework for secure key distribution and authentication in next-generation mobile and distributed quantum networks.
The decoy-state Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol is widely regarded as the de facto standard for practical implementations. On the receiver side, passive basis choice is attractive because it significantly reduces the need for random number generators and eliminates the need for optical modulators. Despite these advantages, a finite-key analytical security proof for the decoy-state BB84 protocol, where the basis is chosen passively with a biased probability, has been lacking. In this work, we present a simple analytical finite-key security proof for this setting, yielding a closed-form secret-key rate formula that can be directly evaluated using experimentally accessible parameters. Numerical simulations show that the key rates of passiveand active-measurement implementations are nearly identical, indicating that passive measurement does not compromise key-generation efficiency in practical QKD systems.
Quantum key distribution (QKD) is a cornerstone of secure communication in the quantum era, yet most existing protocols are designed for point-to-point transmission, limiting their scalability in networked environments. In this work, we introduce Loop-Back QKD, a novel QKD protocol that supports both two-party linear configurations and scalable multiuser ring topologies. By leveraging a structured turn-based mechanism and bidirectional pulse propagation, the protocol enables efficient key distribution while reducing the quantum bit error rate (QBER) through a multi-pulse approach. Unlike trusted-node QKD networks, Loop-Back QKD eliminates intermediate-node vulnerabilities, as secret keys are never processed by intermediate nodes. Furthermore, unlike Measurement-Device-Independent (MDI-QKD) and Twin-Field QKD (TF-QKD), which require complex entanglement-based setups, Loop-Back QKD relies solely on direct polarization transformations, reducing vulnerability to side-channel attacks and practical implementation challenges. Additionally, our analysis indicates that multi-pulse Loop-Back QKD can tolerate higher QBER thresholds. However, this increased robustness comes at the cost of a lower key rate efficiency compared to standard QKD schemes. This design choice enhances its robustness against real-world adversarial threats, making it a strong candidate for secure multiuser communication in local and metropolitan-scale quantum networks.