<p>This paper investigates the significant role of Rashba coupling in controlling entanglement within graphene systems. We demonstrate that tuning Rashba coupling allows for effective enhancement or suppression of entanglement, with higher values providing increased robustness against thermal fluctuations. Our results indicate that achieving substantial entanglement may require external factors, such as enhanced Rashba interactions. Notably, while elevated temperatures typically degrade quantum coherence, we find that significant Rashba coupling can preserve quantum correlations, maintaining coherence under challenging thermal conditions. This preservation is essential for improving the fidelity of quantum teleportation processes, which depend on the availability of robust entangled states. Overall, the interplay between Rashba coupling, temperature, and entanglement in graphene carries significant implications for future advancements in quantum technology. The potential to develop stable and efficient quantum information systems utilizing graphene may lead to transformative breakthroughs in quantum computing and communication, underscoring the necessity for continued exploration in this promising area.</p>