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arXiv:2606.19551 · Optical Switching and Networking

Passive-User Bell-State Loop-Back Key Establishment without Quantum Detectors at the User Nodes

Luis Adrián Lizama-Pérez

quant-phcs.CRSubmitted Jun 17, 2026• Announced Jun 19, 2026• 1 citation
v1 · Jun 17, 2026v2 · Aug 19, 2026
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Abstract

We propose and analyze a Bell-state extension of the Loop-Back quantum key distribution architecture for secret-key establishment between two passive users that do not require quantum transmitters or quantum detectors. In the proposed setting, a single active station, Alice, provides the entangled-state infrastructure, retains one qubit of an initially prepared Bell pair, and sends the traveling subsystem through two passive users, denoted by $B_1$ and $B_2$. Each passive user applies a local Pauli operation to the same traveling subsystem, so that the operation observed by Alice is only the effective composition $U_{\mathrm{eff}}=U_2U_1$. After the subsystem returns, Alice performs a Bell-state measurement and, using her private knowledge of the initial Bell state, deterministically identifies the effective Pauli operation. However, the individual factors $U_1$ and $U_2$ remain algebraically hidden from Alice whenever the local choices are uniformly and independently selected. The public effective operation acts as a parity-like constraint: each passive user can infer the operation applied by the other from its own private choice, while the active station learns only the global composition. This construction transfers the essential distributed-transformation mechanism of passive-user Loop-Back QKD to the entangled-state regime. Unlike single-qubit passive-user schemes, whose useful events are intrinsically post-selected, the Bell-state version is limited primarily by the success probability of the Bell-state measurement. We discuss the algebraic structure of the protocol, its interpretation as an infrastructure-assisted mediated key-establishment mechanism, and the physical assumptions required to protect passive Pauli modulators against active injection or Trojan-horse-type attacks.

Journal reference
Optical Switching and Networking, 62 (2026) 100892
DOI
10.1016/j.osn.2026.100892

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We propose and analyze a Bell-state extension of the Loop-Back quantum key distribution architecture for secret-key establishment between two passive users that do not require quantum transmitters or quantum detectors. In the proposed setting, a single active station, Alice, provides the entangled-state infrastructure, retains one qubit of an initially prepared Bell pair, and sends the traveling subsystem through two passive users, denoted by B1B_1B1​ and B2B_2B2​. Each passive user applies a local Pauli operation to the same traveling subsystem, so that the operation observed by Alice is only the effective composition Ueff=U2U1U_{\mathrm{eff}}=U_2U_1Ueff​=U2​U1​. After the subsystem returns, Alice performs a Bell-state measurement and, using her private knowledge of the initial Bell state, deterministically identifies the effective Pauli operation. However, the individual factors U1U_1U1​ and U2U_2U2​ remain algebraically hidden from Alice whenever the local choices are uniformly and independently selected. The public effective operation acts as a parity-like constraint: each passive user can infer the operation applied by the other from its own private choice, while the active station learns only the global composition. This construction transfers the essential distributed-transformation mechanism of passive-user Loop-Back QKD to the entangled-state regime. Unlike single-qubit passive-user schemes, whose useful events are intrinsically post-selected, the Bell-state version is limited primarily by the success probability of the Bell-state measurement. We discuss the algebraic structure of the protocol, its interpretation as an infrastructure-assisted mediated key-establishment mechanism, and the physical assumptions required to protect passive Pauli modulators against active injection or Trojan-horse-type attacks.
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To address the low qubit efficiency and high user-side operational complexity in existing quantum key agreement schemes, this paper proposes a high-efficiency and lightweight quantum key agreement scheme based on Bell states. The scheme is constructed upon a time-reversed EPR architecture, in which a quantum server performs entangled-state preparation and Bell state measurement. Furthermore, a bidirectional decoy photon mechanism is incorporated into the architecture to achieve eavesdropping detection. By exploiting the completeness and orthogonality of the Bell basis, the scheme introduces an encoding mechanism based on local Pauli operations, enabling a single Bell state to carry 2 bits of key information and thereby realizing dense coding, which improves qubit efficiency. Meanwhile, users are only required to perform single-qubit operations, which reduces the quantum operational requirements on the user side. Based on the properties of Bell states, this paper derives the mapping relationship between local Pauli operations and Bell state measurement outcomes. Experimental results on the SpinQ Gemini quantum computing platform are consistent with the theoretical analysis, verifying the feasibility of the proposed scheme. In addition, security analysis shows that, owing to the bidirectional decoy photon mechanism, the scheme can resist various quantum attacks. The proposed scheme combines high efficiency with a lightweight implementation, reducing quantum hardware requirements on the user side and network deployment costs, thereby providing a cost-effective solution for practical quantum key agreement.
In the domain of quantum communication, cryptographic protocols often require users to have access to trusted qubit sources or detectors. Recently, it was shown that on an architecture called the Qline, several protocols can equivalently be performed by parties capable only of single-qubit rotations. In this work, we introduce two composably secure constructions that together show how in most quantum cryptographic protocols, parties traditionally required to perform trusted qubit preparation or measurement can delegate these tasks to an untrusted provider and instead rely on a trusted single-qubit rotation device. Our first construction implements single-qubit measurement and is universally applicable across any context. In contrast, our second construction, which addresses qubit preparation, relies on specific assumptions regarding the underlying protocol. We show, however, that these assumptions are inherently satisfied by the vast majority of common quantum cryptographic protocols. A notable consequence of our results is the formal validation of the Qline as a versatile architecture capable of supporting a wide range of single-qubit protocols.