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Entropy

Three-Basis Loop-Back QKD: A Passive Architecture for Secure and Scalable Quantum Mobile Networks

Luis Adrián Lizama-Pérez, Patricia Morales

Published Dec 11, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.3390/e27121249

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arXiv:2412.02944•Physica Scripta•Dec 31, 2025•2 citations
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.
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.
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.
Abstract We report the implementation of a quantum key distribution (QKD) system over a three-user fiber-optic network in which each user employs an identical bidirectional transceiver, with a single asymmetric interferometer shared between the encoding and decoding paths to reduce duplicated optical resources at the node level. The three users-Alice, Bob, and Charlie-are interconnected through a passive circulator-based hub built from 3-port optical circulators, which enables secure key exchange between any pair of them without active switching or a trusted intermediary. Each user is connected to the central circulator via standard telecom fiber links of 10-15 km, resulting in effective inter-user distances of 20-25 km. We employed the BB84 protocol with a two-decoy-state method (weak and vacuum) for secure key generation. For each user pair, sifted keys of 10610^6106 bits were processed with a composable security parameter ε∼10−8\varepsilon \sim 10^{-8}ε∼10−8 . Secret key lengths were evaluated using three approaches: (1) theoretical estimation based on measured quantum bit error rate (QBER) and gains, assuming an error correction efficiency of 1.16; (2) experimental post-processing using Winnow; and (3) experimental post-processing using Cascade. All links achieved low QBERs and yielded positive secret key lengths. Cascade consistently produced longer final keys due to its higher reconciliation efficiency. These results demonstrate the feasibility of a resource-sharing bidirectional node architecture for secure multi-user quantum communication using passive circulator-based routing.
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, B1B_1B1​ and B2B_2B2​ , apply independently selected polarization rotations R(±π/8)R(\pm \pi /8)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, XXX , and ZZZ components and no YYY component. Both recover the ideal conclusive-event probability Pconc=1/4P_{\textrm{conc}}=1/4Pconc​=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/2e_{1,\mathrm p}=3e_{1,\mathrm b}/2e1,p​=3e1,b​/2 , together with a low-error robust angular bound e1,p≤κrote1,be_{1,\mathrm p}\le \kappa _{\textrm{rot}}e_{1,\mathrm b}e1,p​≤κrot​e1,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.
Unlike currently implemented encryption schemes, Quantum Key Distribution provides a secure way of generating and distributing a key among two parties. Although a multitude of research platforms has been developed, the integration of QKD units within classical communication systems remains a tremendous challenge. The recently achieved maturity of integrated photonic technologies could be exploited to create miniature QKD add-ons that could extend the primary function of various existing systems such as mobile devices or optical stations. In this work we report on an integrated optics module enabling secure short-distance communication for, e.g., quantum access schemes. Using BB84-like protocols, Alice's mobile low-cost device can exchange secure key and information everywhere within a trusted node network. The new optics platform (35×20×8mm) compatible with current smartphone's technology generates NIR faint polarised laser pulses with 100MHz repetition rate. Fully automated beam tracking and live basis-alignment on Bob's side ensure user-friendly operation with a quantum link efficiency as high as 50% stable over a few seconds.
Abstract The BB84 quantum key distribution (QKD) protocol sets the foundation for achieving secure communication against quantum threats. Since its inception, significant advancements have aimed towards frugal experimental implementations with enhanced security. In this paper, we report a passive polarization encoded BB84 protocol. By passively and randomly encoding the polarization states, the setup avoids active modulation and simplifies design with security standards analogous to entanglement-based QKD. The heralding of a probabilistic single-photon source ensures an extremely low probability of multi-photon emissions evading photon number-splitting attacks. The quality of the single-photon source and thus, the QKD setup is certified by the second-order correlation function, g (2) (0) = 0.006 ± 0.0002. Our protocol provides an optimisation trade-off between the conventional BB84 and the BBM92 protocol. The advantage relies on using fewer detectors (compared to the BBM92 protocol) and no reliance on active quantum random number generators (compared to the standard BB84) to drive Alice’s encoding scheme. Our implementation achieves a quantum bit error rate of 7% and a secure key rate of 5 kbps.