Optimal Conversion from Continuous- to Discrete-Variable Bipartite Entanglement

Discrete-variable (DV) entanglement is crucial for numerous quantum applications, yet its deterministic generation in bosonic systems remains experimentally challenging. In contrast, the continuous-variable (CV) entanglement can be produced efficiently. We propose two optimal schemes for converting CV bipartite entanglement into DV entanglement using only local operations and classical communication. The first scheme extracts maximally entangled qubit pairs at the theoretically optimal rate, while the second yields an ensemble of maximally entangled qudit pairs with maximal average entanglement. Compared to the literature, our schemes require at least quadratically fewer measurement operators. Surprisingly, despite employing only binary measurements, our approach can succeed in a finite round of measurement on average even though the CV resource is infinite dimensional. Our schemes improve the feasibility of DV-based quantum technologies on bosonic platforms.