A Survey of OAM-Encoded High-Dimensional Quantum Key Distribution: Foundations, Experiments, and Recent Trends

High-dimensional quantum key distribution (HD-QKD) enhances information efficiency and noise tolerance by encoding data in large Hilbert spaces. The orbital angular momentum (OAM) of light provides a scalable basis for such encoding and supports high-dimensional photonic communication. Practical OAM-based implementations remain constrained by challenges in state generation, transmission, and detection. This survey offers a consolidated overview of OAM-encoded HD-QKD, outlining fundamental principles, representative experiments, and system-level limitations. Recent progress in hybrid encodings, mode sorting, adaptive optics, and TF, CV, MDI, and DI frameworks is summarized with emphasis on practical feasibility.

💡 Research Summary

This survey paper provides a comprehensive overview of high-dimensional quantum key distribution (HD-QKD) encoded in the orbital angular momentum (OAM) of light. It systematically consolidates the foundational principles, experimental progress, practical limitations, and recent research trends in this field.

The paper begins by establishing the context: the threat posed by quantum computing to classical public-key cryptography and the role of QKD as a long-term secure solution. It highlights the limitations of conventional two-dimensional QKD (like BB84), particularly its restricted secret key rate (SKR) and sensitivity to noise. HD-QKD is introduced as a promising avenue to overcome these limitations by encoding information in quantum states residing in a Hilbert space of dimension d > 2. This allows each photon to carry up to log₂(d) bits of information, thereby increasing the SKR. Crucially, HD-QKD also offers enhanced error tolerance, with the tolerable Quantum Bit Error Rate (QBER) threshold increasing with the dimension d.

The core of the paper explains why OAM is an ideal physical degree of freedom for HD-QKD. OAM modes form a discrete, theoretically unbounded basis of orthogonal states, providing a scalable platform for high-dimensional encoding. The foundational section details the general QKD workflow (quantum exchange, sifting, parameter estimation, information reconciliation, privacy amplification) and adapts it for the high-dimensional case. It presents key performance metrics, analyzing the secret-key fraction formula for a d-dimensional BB84 protocol and demonstrating how higher dimensions raise the QBER threshold for a positive SKR. A simple link model incorporating channel loss and detector dark counts is used to illustrate practical constraints on the achievable SKR.

The survey then reviews representative experimental demonstrations of OAM-based QKD, categorizing them into prepare-and-measure and entanglement-based schemes. Following this, a critical analysis of practical system-level limitations is presented, structured around the three key stages: state generation (e.g., efficiency and accuracy of creating OAM modes using spatial light modulators), transmission (e.g., channel-induced effects like atmospheric turbulence, fiber modal dispersion, and crosstalk), and detection (e.g., challenges in efficient and accurate sorting and detection of multiple OAM modes).

A significant portion of the paper is dedicated to emerging research directions aimed at addressing these challenges and enhancing system performance. These trends include: the development of hybrid encodings that combine OAM with other degrees of freedom (like polarization) for increased robustness; advances in mode-sorting techniques and the application of adaptive optics to compensate for atmospheric distortions; and the integration of OAM-based encoding into advanced QKD frameworks. The latter encompasses proposals for Twin-Field (TF) QKD to extend range, Continuous-Variable (CV) QKD with spatial-mode multiplexing, and the exploration of Measurement-Device-Independent (MDI) and Device-Independent (DI) QKD protocols to bolster security against detector-side attacks. The paper notes that many of these advanced concepts are still in the proposal or early experimental phase.

In conclusion, the survey affirms the strong theoretical potential of OAM-encoded HD-QKD for achieving higher secret key rates and greater resilience in noisy environments. However, it underscores that practical deployment is currently constrained by significant engineering challenges related to state manipulation, channel robustness, and detection complexity. The path forward likely involves hybrid multi-degree-of-freedom approaches and the continued development of innovative protocols to bridge the gap between theoretical promise and practical, real-world implementation.