This paper offers a thorough investigation into quantum cryptography, a security paradigm based on the principles of quantum mechanics that provides exceptional guarantees for communication and information protection. The study covers the fundamental principles of quantum cryptography, mathematical modelling, practical applications, and future prospects. It discusses the representation of quantum states, quantum operations, and quantum measurements, emphasising their significance in mathematical modelling. The paper showcases the real-world applications of quantum cryptography in secure communication networks, financial systems, government and defence sectors, and data centres. Furthermore, it identifies emerging domains such as IoT, 5G networks, blockchain technology, and cloud computing as promising areas for implementing quantum cryptographic solutions. The paper also presents avenues for further research, including post-quantum cryptography, quantum cryptanalysis, multi-party quantum communication, and device-independent quantum cryptography. Lastly, it underscores the importance of developing robust infrastructure, establishing standards, and ensuring interoperability to facilitate widespread adoption of quantum cryptography. This comprehensive exploration of quantum cryptography contributes to the advancement of secure communication, information protection, and the future of information security in the era of quantum technology.