Advantage of Deterministic Entanglement Transmission on Gaussian-State Quantum Networks

The promising future of the quantum internet hinges on how we scale entanglement distribution on quantum networks (QN). Classical entanglement percolation (CEP) offers a simple approach for this but is limited by "classical" scaling laws, while deterministic entanglement transmission (DET) leverages the determinacy of quantum protocols to achieve a more effective "quantum" scaling. This advantage is, however, unexplored for Gaussian-state QNs, where the infinite-dimensional, continuous-variable states are often required to be first prepared into qubits or qudits via additional conversions. This overhead raises a question: can DET's quantum advantage survive in a practical Gaussian-to-qudit conversion process? To answer this, we analyze both DET and CEP across a spectrum of conversion strategies, from best-case theoretical limits to probabilistic, practical projections. We find that DET's superiority is robust: even a DET scheme burdened by the overhead of practical projective conversions consistently outperforms CEP endowed with theoretically perfect conversion. Our work thus provides a possible roadmap, demonstrating that the quantum-native approach of DET could be the key to unlocking the potential of long-range quantum communication.