Bit thread, entanglement distillation, and entanglement of purification

We investigate the relations between bit thread, entanglement distillation and entanglement of purification in the holographic framework. Specifically, we give a bit thread interpretation for the one-shot entanglement distillation (OSED) tensor network, which can be understood as reconstructing the geometric structure of the bulk spacetime from the entanglement information of the boundary quantum system through the "surface growth scheme". Moreover, based on this, we naturally obtain the bit thread interpretation of the holographic entanglement of purification (EoP), which eliminates some inconsistencies in the existing interpretations.