Entanglement-Enhanced Information Dynamics in Triple-Coin Discrete-Time Quantum Walks

This work investigates a discrete-time quantum walk on a one-dimensional lattice driven by three entangled coins, each initialized via a Hadamard operator. The walker moves only when all three coins yield identical outcomes (HHH or TTT), coupling an 8-dimensional coin Hilbert space to the position degree of freedom. We analyze fully separable, fully entangled, and intermediate initial coin states, computing the von Neumann entropy of reduced subsystems to derive the mutual information between coin and position over successive steps. Our results demonstrate that initial tripartite entanglement significantly accelerates the growth of mutual information and enhances coin-position correlations compared to separable initial conditions. Notably, GHZ-type entangled states exhibit non-monotonic short-time dynamics due to interference, yet ultimately yield up to 18% higher mutual information by the tenth step. These findings underscore the role of pre-walk entanglement as a resource for controlling information flow and spatial spreading in quantum-walk-based protocols, with implications for quantum transport, state transfer, and correlation engineering.