Quantum Information Processing in Networked Systems: Entanglement Dynamics and Temporal Correlations

We develop a comprehensive theoretical framework for analyzing quantum information flow in networked quantum systems with emphasis on entanglement distribution and temporal correlation structures. Drawing from recent applications in real-time sensing and detection systems, we formulate a general mathematical model that describes how quantum correlations propagate through network topologies and evolve over time. The framework incorporates decoherence effects, network connectivity constraints, and measurement-induced state collapse to provide realistic bounds on information transmission capabilities. We derive analytical expressions for entanglement generation rates, fidelity preservation across network hops, and temporal correlation decay under various noise models. The theory establishes fundamental limits on the capacity of quantum networks to maintain coherent information transfer and identifies optimal network architectures for specific correlation preservation requirements. We extend our analysis to adaptive network configurations where topology can be dynamically adjusted based on environmental conditions or information priorities. The theoretical results provide design principles for quantum communication protocols, distributed quantum sensing arrays, and real-time quantum-enhanced detection systems, bridging fundamental quantum information theory with practical networked applications.