Measurement-device-independent multi-party quantum secure direct communication

As one of the most important branches of quantum information science, quantum communication is known for its unconditional security and efficiency. Nevertheless, the practical security of quantum key distribution protocols and quantum secure direct communication protocols is challenged due to the imperfections in experimental devices. Despite significant progress in theoretical and experimental research on the MDI-QSDC Protocol, challenges and unresolved issues remain. For example, further enhancing the scalability and system complexity of the protocol to meet the demands of large-scale quantum networks is necessary. In this paper, we propose a multi-party MDI-QSDC scheme based on multi-degree-of-freedom hyperentangled photons. Compared to the original MDI-QSDC protocol, our protocol allows multiple parties to participate in the information transmission process. For example, for four communicating parties, we can encode the information of three independent degrees of freedom so that each photon of each degree of freedom can transmit 2 bits of information. Moreover, all measurement tasks are performed by the fifth party, which can be untrusted or even completely controlled by eavesdroppers. The protocol is resistant to all possible attacks from imperfect measurement devices. It can eventually be extended to arbitrary degrees of freedom, allowing multiple parties to participate.