Abstract
—Large Language Models (LLMs) have demonstrated strong potential in clinical reasoning, but their scale and cost prevent deployment on resource-constrained telemedicine edge networks. Small language models (SLMs) offer efficiency, yet their limited semantic depth hinders accurate diagnostic support. This gap motivates a Federated Learning (FL) approach, where distributed SLMs collaborate under supervision, while Knowledge Distillation (KD) transfers reasoning from LLMs to sustain accuracy. However, today's SLM deployments still lack agentic coordination, leaving clinical workflows fragmented. Agentic communication security relies on classical cryptography that cannot withstand quantum adversaries. To address these challenges, we propose Q-SAFe, a four-phase scheme that integrates federated SLM training, agentic orchestration, and Post-Quantum Cryptography (PQC) algorithms. Patient and hospital agents are registered, and are collaboratively trained with Fed-erated Proximal (FedProx) and KD strategy. They are connected through authenticated cross-layer handshakes, and protected by Post Quantum Cryptography (PQC) scheme for secure record exchange. Validations show that Q-SAFe sustains clinical-grade responsiveness (≤ 200 ms latency under 300 users), achieves stable convergence (≈ 85% accuracy within 50 rounds), and imposes only 3 KB per-exchange cryptographic overhead, making it suitable for practical edge deployments. The code is available at https://github.com/Mahdiya-Nishat/Q-SAFe.