Federated Learning (FL) enables collaborative training of models across institutions without centralizing sensitive data, making it well-suited for privacy-concerned applications, such as medical imaging. To protect FL model updates during secure aggregation, additive masking is commonly employed. However, its underlying classical key establishment is only computationally secure. On the other hand, physics-based Information-Theoretically Secure (ITS) key exchange introduces practical constraints: finite key generation rates and time-limited storage severely limit throughput and sustained training of uncompressed models. In this work, we address this bottleneck by developing an FL framework that integrates frozen backbones, knowledge distillation, and quantization. These techniques reduce communication payload and, consequently, key material consumption. Moving beyond simulation, we benchmark this framework on a real physics-based key distribution testbed involving a chest X-ray classification application. Our results show that key usage can be reduced by $\sim$35$\times$ while maintaining predictive accuracy. This prevents buffer depletion and key expiration, enabling sustainable FL training under physical key generation constraints.

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