We introduce QEDRA (Quantum-Entangled Decentralized Reasoning and Aggregation), the first practical framework that simultaneously addresses ultra-scarce data regimes ( \(n_k < 20\) ), quantum-scale security threats, and ethical requirements in healthcare AI. Unlike conventional federated learning systems that sacrifice privacy for utility, QEDRA leverages 9-qubit W-state entanglement ( \(|\textrm{W}_9\rangle = \frac{1}{\sqrt{9}}\sum _{i=1}^9|1_i\rangle \) ) to generate semantically aware noise that improves utility while providing formal \((\epsilon ,\delta )\) -differential privacy guarantees ( \(\epsilon = 0.08\) –0.17, \(\delta = 10^{-16}\) ). QEDRA’s NISQ-compatible architecture integrates quantum physics with neuro-symbolic reasoning through four key innovations: (1) Quantum-Entangled Differential Privacy (QEDP) that breaks the classical privacy-utility trade-off; (2) Neuro-Symbolic Swarm Intelligence with Quantum-Entangled PSO (QEPSO) for multimodal fusion; (3) Privacy-Aware LLM Fine-Tuning with symbolic guardrails; and (4) Verifiable Ethical Governance via Quantum Multi-Party Computation. Validated on MIMIC-IV, QEDRA achieves 87.0% F1-score (45% higher than FedAvg), 0.4% attack success rate, and 99% fault recovery under decoherence ( \(p_{\text {dep}} = 0.005\) ), all while maintaining \(T_{\text {round}} < 2.4\) s latency through BB84-QKD-secured channels. Critically, QEDRA is engineered for real-world deployment on IBM 127-qubit Eagle processors ( \(QV=128\) ) with seamless classical fallback when entanglement fidelity drops below \(F < 0.98\) . By co-designing quantum circuits with classical resilience, QEDRA delivers provable trustworthiness without performance compromise, establishing a new standard for quantum-resilient, ethically grounded AI in resource-constrained medical environments.