Cryptographic algorithm for multi-path distribution of entangled states of orbital angular momentum based on Fibonacci values

Drawing inspiration from the Fibonacci sequence and its complementary Lucas sequence, this paper introduces an innovative encryption and decryption algorithm tailored for multi-path quantum key distribution. The algorithm capitalizes on the high-quality orbital angular momentum entangled states, harnessing the mathematical elegance of Fibonacci numbers to construct block diagonal matrices. These matrices serve as the foundation for the simultaneous execution of key distribution across multiple communication paths in a structured block distribution format. The encryption process is facilitated through a combination of linear mappings, employing specific transition matrices to manage the cryptographic flow. The security underpinning of this method is firmly rooted in the Heisenberg Uncertainty Principle, a fundamental tenet of quantum mechanics, which ensures the confidentiality and integrity of the quantum communication channel. This approach paves the way for a novel encryption paradigm, fortifying the security framework of quantum communication networks.