Entanglement distillation of bosonic qudits encoded in two cavities

High-quality entanglement is crucial for advancing quantum computation and communication. Entanglement distillation serves this purpose by converting multiple low-fidelity Bell pairs into fewer high-fidelity ones, using only local quantum operations and classical communication. This process can be made more hardware-efficient using a single pair of bosonic systems, whose high-dimensional Hilbert space allows for the storage of a large amount of entanglement. We present a protocol to distill a noisy state with a large amount of entanglement between two cavities into a lower-dimensional high-fidelity entangled state, using operations native to the bosonic systems. We show that this protocol successfully enhances the fidelity of the entangled states in the presence of loss and dephasing errors.