Building upon our pioneering work on high-dimensional entangled states [1], this project aims to investigate further into the theoretical and experimental aspects of quantum information processing based on high-dimensional systems, with a focus on advancing quantum communication and sensing technologies. High-dimensional quantum systems, or qudits, promise significant advantages over traditional qubit systems, including increased information capacity, enhanced security in quantum cryptography, and improved resilience to noise and decoherence [2,3]. However, several open questions and practical challenges remain in fully exploiting these advantages. 

One of the central theoretical challenges lies in developing efficient quantum algorithms that exploit the richer Hilbert space of qudits. While qudits theoretically enable more complex computations and higher data capacity, practical implementations require novel approaches to quantum gate design and error correction tailored to high-dimensional systems [4,5]. Understanding how to construct universal sets of quantum gates for qudits and how to perform high-fidelity operations remains an open question critical to the advancement of qudit quantum computing. 

In quantum communication, higher-dimensional entangled states have been shown to enhance security against eavesdropping and increase the channel capacity of quantum key distribution protocols [6]. However, the practical realization of these protocols faces limitations due to challenges in the generation, transmission, and detection of high-dimensional entangled photons. Issues such as mode dispersion in optical fibres, sensitivity to environmental perturbations, and the complexity of high-dimensional state measurement impede scalability and real-world deployment [7]. This project will explore innovative schemes to circumvent these challenges, such as leveraging adaptive optics, encoding methods like orbital angular momentum modes, path and time bins, and integrated photonic circuits to generate and control high-dimensional entangled states with greater stability and efficiency [8,9]. 

The practicality of realising qudit systems is also a significant hurdle in quantum sensing applications. High-dimensional entangled states can, in principle, improve sensitivity and resolution beyond the standard quantum limit [10]. Yet, implementing these states in practical sensors is hindered by technical difficulties in state preparation and detection, as well as vulnerability to experimental imperfections. There will be scope in the project to investigate new schemes that can operate under realistic conditions, potentially incorporating hybrid systems that combine different physical modalities to enhance robustness while retaining the advantages offered by high-dimensional entanglement [11]. 

By addressing these theoretical and practical challenges, this project seeks to push the boundaries of quantum secure communication and quantum networking. Our research will contribute to the development of new quantum algorithms, error correction methods, and experimental techniques that make high-dimensional quantum systems more accessible and functional.