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Big data analytics encounters scalability, latency, and privacy challenges, especially within real-time streaming contexts. We propose the Privacy-Aware Quantum Stream (PAQS), a distributed framework inspired by quantum principles, to overcome these obstacles. PAQS utilizes quantum superposition to effectively represent high-dimensional data, quantum entanglement for sophisticated correlation analysis and anomaly detection, and federated learning combined with homomorphic encryption to maintain privacy without compromising performance. The adaptive switching mechanism balances quantum-inspired and classical processing according to sensitivity and dimensionality criteria. Experiments are conducted on three datasets—OpenStreetMap, MIMIC-III, and KITTI, which show significant improvements: a throughput of 2. 53 TB/sec, a 60 % reduction in latency, an anomaly detection accuracy of 92. 3 %, and an 85. 4 % decrease in privacy violations when compared to baselines. These findings validate that PAQS provides consistent, secure, and scalable real-time analytics, positioning it as a strong solution for smart cities, healthcare, and autonomous transportation applications.