Device-Independent Ternary Quantum Key Distribution Protocol Based on the Impossible Colouring Game

We propose a Ternary Device-Independent Quantum Key Distribution (TDIQKD) protocol based on the two-party Impossible Colouring pseudo-telepathy game, using maximally entangled qutrit states to enable secure key generation between distant parties. The protocol makes use of non-contextuality from the Kochen-Specker theorem, providing a quantum advantage in a task that is classically unachievable, and eliminates reliance on assumptions about the internal workings of quantum devices. A specially designed qutrit quantum circuit is employed for state preparation, and security is rigorously analyzed through a composable framework using smooth minimum entropy, von Neumann entropy, and Shannon entropy. The protocol achieves optimal key rate in the ideal case and maintains security under significant noise, with a finite-key analysis supporting practical deployment. The protocol is secure within an adequate security framework and demonstrates a higher key generation rate compared to standard QKD protocols, emphasizing the potential of high-dimensional quantum systems for secure communication.