Large-scale quantum networks depend on the efficient distribution of entangled pairs between distant nodes. However, state-of-the-art solutions rely on restrictive operational assumptions, incur prohibitive computational complexity, and optimize metrics misaligned with application needs. This paper addresses the entanglement distribution problem introducing four pivotal advances. First, since the primary application of quantum communication is private information transmission, we derive the Ensemble Capacity, a novel metric that quantifies the private classical information enabled by entanglement distribution. Second, we propose a generalized formulation of the Entanglement Distribution Problem that allows arbitrary sequencing of entanglement swapping and purification, removing the structural restrictions of prior models. Third, to navigate the resulting combinatorial space, we introduce a dynamic programming-based hypergraph generation algorithm that preserves exact, continuous fidelities, avoiding quantization, while pruning sub-optimal sequences in advance. Finally, we integrate these solutions into CODE, a two-tier orchestration framework enabling near-real-time network operation. Extensive evaluations show that our approach achieves higher private information capacity and significantly lower computational complexity than existing solutions, while meeting the sub-second latency requirements of dynamic quantum network operation.

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