Having multiple Bell pairs shared by distant quantum registers provides a key resource for both quantum networks and distributed quantum computing. In this paper, we present a protocol for parallelized Bell-pair generation that uses the phase of a coherent light pulse to encode a qudit, enabling the simultaneous generation of multiple Bell pairs. By encoding a qudit in a basis of light-matter Schrödinger's cat states, the loss of a photon in transit can be detected through an $XX$ parity syndrome, allowing the backaction due to the lost photon to be deterministically corrected through single-qubit rotations. The protocol presented here is compatible with existing technologies in both optical and microwave (circuit QED) architectures, supporting near-term implementation across diverse quantum platforms.

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• Entanglement production
• Quantum information processing with continuous variables
• Quantum networks