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<p>Measurement-device-independent quantum secure direct communication (MDI-QSDC) mitigates measurement-device side-channel vulnerabilities, yet existing schemes often suffer from limited capacity and low efficiency. In this work, we propose an MDI-QSDC protocol based on polarization-spatial hyperentangled Bell states. The protocol involves two rounds of hyperentangled Bell-state measurements (HBSMs) performed by an untrusted relay to enable entanglement-swapping-assisted direct message transmission. Decoy photons are inserted in the first round for channel checking, while a pseudo-random function (PRF) is adopted to select communication particle positions and to control local Pauli operations to encode messages and hide roles. The receiver performs the corresponding Pauli corrections based on the announced measurement outcomes and their locally prepared states to recover the secret message. Each successful hyperentangled pair carries 4 classical bits. Under typical settings (e.g., PRF modulus <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(m = 4-8\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>m</mi> <mo>=</mo> <mn>4</mn> <mo>-</mo> <mn>8</mn> </mrow> </math></EquationSource> </InlineEquation> and a decoy ratio of 10–20%), the expected communication efficiency is 42–49%, accounting for the probabilistic nature of HBSMs in linear-optical implementations. Compared with representative MDI-QSDC protocols, the proposed scheme achieves higher capacity with competitive efficiency while maintaining moderate implementation complexity. The protocol is particularly suitable for metropolitan-scale, node-based, and free-space/hybrid quantum networking scenarios, where the spatial degree of freedom can be realized via stable path encoding or other mode-controlled implementations.</p>

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Measurement-device-independent quantum secure direct communication using polarization–spatial hyperentanglement and PRF encoding

  • 期刊论文

  • 发表日期：

    2026年4月13日

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  • Dao-Bei Song,
  • Ri-Gui Zhou,
  • Lin-Tao Du

摘要

Measurement-device-independent quantum secure direct communication (MDI-QSDC) mitigates measurement-device side-channel vulnerabilities, yet existing schemes often suffer from limited capacity and low efficiency. In this work, we propose an MDI-QSDC protocol based on polarization-spatial hyperentangled Bell states. The protocol involves two rounds of hyperentangled Bell-state measurements (HBSMs) performed by an untrusted relay to enable entanglement-swapping-assisted direct message transmission. Decoy photons are inserted in the first round for channel checking, while a pseudo-random function (PRF) is adopted to select communication particle positions and to control local Pauli operations to encode messages and hide roles. The receiver performs the corresponding Pauli corrections based on the announced measurement outcomes and their locally prepared states to recover the secret message. Each successful hyperentangled pair carries 4 classical bits. Under typical settings (e.g., PRF modulus \(m = 4-8\) m = 4 - 8 and a decoy ratio of 10–20%), the expected communication efficiency is 42–49%, accounting for the probabilistic nature of HBSMs in linear-optical implementations. Compared with representative MDI-QSDC protocols, the proposed scheme achieves higher capacity with competitive efficiency while maintaining moderate implementation complexity. The protocol is particularly suitable for metropolitan-scale, node-based, and free-space/hybrid quantum networking scenarios, where the spatial degree of freedom can be realized via stable path encoding or other mode-controlled implementations.