Investigating the impact of relative entropy of coherence on end-to-end fidelity in quantum networks under different noise models

Ensuring high end-to-end fidelity is crucial for quantum networks, yet the impact of relative entropy of coherence on end to end fidelity remains unexplored. This study investigates how amplitude damping, and depolarizing noise affect coherence and fidelity as distance increases, with and without entanglement purification. Using Kraus operators, we model noise and compute relative entropy of coherence. By applying curve fitting, we extract coherence decay time and integrate it into the end-to-end fidelity equation, deriving a new analytical expression. Results show that noise models significantly impact fidelity, with purification improving performance but with varying effectiveness. These findings provide new insights into coherence-fidelity relationships, emphasizing the need for coherence-aware strategies in quantum routing.