Abstract: Entanglement purification/distillation is a quintessential task of a quantum network. Simple bipartite purification schemes use two or more noisy entangled pairs to probabilistically improve the fidelity of one pair by performing local operations and classical operations across the two parties sharing the pairs. However, these are asymptotically inefficient in the conversion of noisy input entanglement into higher fidelity output entanglement. Bennett et al. established the connection between one-way entanglement purification protocols and quantum error correction. In this talk, we will begin by reviewing this connection and discuss an equivalent protocol by Wilde et al. to purify Bell pairs. Then we will use the stabilizer formalism to generalize the protocol to GHZ states of any size. As part of this process, we will discuss a new insight on Pauli measurements on GHZ states. We will discuss the application of such protocols to quantum repeaters based on trapped ions. We will finally combine this protocol with a scheduling strategy for a linear chain of repeaters that determines the optimal policy between entanglement distillation and entanglement swapping at each repeater. The goal here is to maximize the total distillable entanglement from the final end-to-end pairs. If time permits, we will briefly discuss the concatenation of GKP codes with good quantum LDPC codes that has connections to GKP-based quantum repeater architectures.