# High-Dimensional and Multi-Intensity One-Photon-Interference Quantum Secure Direct Communication
## 5 Conclusions  
In this work, we present a high-dimensional one-photon-interference quantum secure direct communication protocol (HDOPI-QSDC), that generalizes the original one-photon-interference quantum secure direct communication framework to high-dimensional encoding. This advancement results in an enhanced secrecy channel capacity and an extended transmission distance, while maintaining a measurement-device-independent characteristic even though it involves the imperfect measurement devices of legitimate users. The security of the protocol is analyzed utilizing the quantum wiretap channel theory, and the secrecy channel capacity is derived. Furthermore, its resistance to common quantum threats is examined. Numerical simulations demonstrate that the HDOPI-QSDC protocol not only achieves a higher secrecy capacity but also improves the transmission distance by up to approximately 60 km compared to its predecessors, reaching a maximum range of 494 km, which effectively doubles the communication length of traditional protocols. These promising results suggest that our protocol holds potential for future applications, such as intercity quantum communications in government, finance, and healthcare sectors, where its extended range and high capacity could reduce reliance on quantum repeaters. Leveraging the merit of its deterministic information transmission, QSDC integrated with classic or post-quantum cryptography could boost the bandwidth of secure communication and provide an extra layer of protection by transferring only the secret keys via quantum channels, ensuring the hybrid system remains resistant to both quantum and classical adversaries. However, the proposed protocol is subject to several key constraints that require further investigation. First, our security analysis assumes an infinite block length, which simplifies the derivation of the secrecy capacity by neglecting the statistical fluctuations introduced by finite block lengths in the estimation of channel parameters. In practice, the finite size of the information block leads to tighter bounds and potentially a lower performance. Second, the protocol also presumes an unlimited number of light intensities in the multi-intensity mode. Although three or four intensities should suffice in real-world systems, a detailed capacity analysis of these limited intensity values is needed. Third, the experimental implementation of our protocol faces significant difficulties, due to its heavy reliance on high-precision phase operations. Achieving adequate one-photon interference visibility requires maintaining phase coherence over long distances, between the independent lasers at [PERSON]'s and [PERSON]'s stations. Consequently, the precise synchronization of remote lasers is critical, and active, continuous phase compensation and stabilization is essential to counter environmental disturbances. Moreover, developing high-efficiency and low-noise single-photon detectors remains a substantial challenge. While recent advancements in optical systems [60, 61], detector performance [62, 63], and protocol optimization [64, 65] have shed light on these experimental hurdles with proof-of-principle demonstrations [66, 67, 68], further innovations will be necessary for the practical deployment of this protocol. Conceptualization, X-J.L. ; formal analysis, X-J.L. and Y-T.L. ; software, X-J.L. ; validation, Y-T.L. ; writing--original draft preparation, Y-T.L. and X-J.L. ; writing--review and editing, X-B.P. and Y-R.Z. ; supervision, G.-L.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China under Grants No. 62471046 and No. 62401324; the Beijing Advanced Innovation Center for Future Chip (ICFC); and the Tsinghua University Initiative Scientific Research Program. Data Availability Statement: Data are contained within the article. **Conflicts of Interest:** The author [PERSON] was employed by the company Future Research Lab, China Mobile Research Institute.