Entanglement Purification Beyond Identical Input

Entanglement purification protocols (EPPs) are essential for quantum communication networks, which are the backbone of fault-tolerant, scalable distributed quantum information processing. While simplifying theoretical studies, the common assumption of identical input is almost never justified in reality. This dissertation investigates entanglement purification with non-identical input from three perspectives: what is fundamentally restricted, what is guaranteed, and how to enhance EPP performance. We first introduce the concept of input-independent universal EPPs and prove no-go theorems for their existence. Despite the no-go theorems, we prove guaranteed improvements that EPPs can achieve, with the 2-to-1 CNOT-based EPP as a canonical example. We also prove the optimal time to apply this EPP in realistic quantum repeater scenarios for typical error models and figures of merit. We then prove that shared randomness, a classical resource, can enhance the performance of an arbitrary $n$-to-1 bilocal Clifford entanglement purification protocol using the strategy of accumulating and shuffling in a multi-source scenario. Altogether, this dissertation offers insights into both the theoretical understanding of EPPs with non-identical input and the practical integration of EPPs into realistic quantum networks.