A rigorous N-qubit theory proves that depolarising noise in stochastic quantum neural networks contracts Pauli read-outs exponentially, enabling robust anomaly detection. On the NSL-KDD dataset, such noise achieves significant adversarial resilience without catastrophic collapse, outperforming noiseless models and classical detectors under FGSM and PGD attacks, with reduced robustness variance and a train-test gap reduction of approximately 0.01.