# Multi-Party Controlled Semi-Quantum Dialogue Protocol Based on Hyperentangled Bell States
## 1 Introduction  
Quantum secure direct communication (QSDC) is a significant branch within the quantum cryptography framework, achieving the transmission of ciphertext directly through a quantum channel without the need for pre-shared keys [1]. In 2003, [PERSON] et al. pioneered the two-step QSDC protocol based on EPR entangled pairs [2], establishing the core criteria of QSDC for the first time: qubits serve as both information carriers and eavesdropping detection, alongside the necessity of a post-selection mechanism for information decoding. To address vulnerabilities associated with measurement devices, the [PERSON] team [3] proposed the first measurement-device-independent (MDI) QSDC protocol in 2020. In the same year, [PERSON] et al. [4] innovatively utilized hyperentangled states of photon polarization-spatial mode dual degrees of freedom (DOF) to construct a high-capacityMDI-QSDC protocol. In recent years, researchers have made milestone progress in experimental studies of QSDC [5; 6]. Particularly noteworthy is [PERSON] et al. 's proposal in 2021 [7] of a QSDC network based on time-energy entanglement and sum-frequency generation, which established a secure quantum entanglement channel over 40 km of fiber by implementing quantum memory functionality through adjustments to circuit delay modules. By 2023, [PERSON] et al. [8] realized the first real-time QSDC network based on computationally secure relays, providing reliable experimental evidence for further research and advancing QSDC towards practical application stages. Quantum dialogue (QD), as a bidirectional extension paradigm of QSDC, facilitates interactive information exchange between two parties over a quantum channel. The QD protocol framework was first introduced by [PERSON] [9] in 2004, which addressed the limitations of one-way communication in QSDC. However, [PERSON] et al. [10] revealed in their 2008 study that QD protocols commonly suffer from information leakage vulnerabilities. This finding spurred research into anti-leakage mechanisms as a core topic. In 2014, the [PERSON] team [11] innovatively introduced EPR pairs as private quantum keys, using dynamic unitary rotations to encrypt transmitted photons in real time, successfully overcoming the issue of information leakage in QD. In 2015, [PERSON] et al. [12] utilized a class of three-qubit W-states and quantum dense coding techniques to achieve a QD protocol with zero information leakage. In 2018, [PERSON] et al. [13] proposed the first controlled quantum dialogue (CQD) protocol with an authentication mechanism, which successfully defended against both internal and external attacks. In 2021, [PERSON] et al. [14] presented an MDI-QD protocol based on hyperentanglement, which effectively eliminated security vulnerabilities and information leakage issues related to measurement devices. In 2023, [PERSON] et al. [15] proposed two efficient fault-tolerant QD protocols tailored for collective noise channels, designing and implementing quantum logic circuits for practical demonstration. [PERSON] et al. [16] proposed a one-step QD protocol based on hyperentanglement, which greatly simplified experimental procedures and reduced message loss due to photon transmission losses. [PERSON] et al. [17] extended QD to quantum communication networks using cluster states, eliminating the need for trusted node assumptions and achieving higher fidelity in transmission. Additionally, in 2025, [PERSON] et al. [18] proposed a rapid quantum dialogue protocol that operates without unitary operations or auxiliary photons. Also in the same year, [PERSON] et al. [19] introduced a counterfactual controlled QD protocol based on entanglement swapping, demonstrating that neither physical transmission of particles nor prior entanglement between remote participants is required, significantly enhancing system security. The engineering deployment of quantum communication systems faces core bottlenecks in the high cost and low accessibility of quantum devices. To address these challenges, [PERSON] et al.