Entanglement Distribution in Lossy Quantum Networks

Entanglement distribution is essential for unlocking the potential of distributed quantum information processing. We consider an $N$-partite network where entanglement is distributed via a central source over lossy channels, and network participants cooperate to establish entanglement between any two chosen parties under local operations and classical communication (LOCC) constraints. We develop a general mathematical framework to assess the optimal average bipartite entanglement shared in a lossy distribution, and introduce a tractable lower bound by optimizing over a subset of single-parameter LOCC transformations. Our results show that probabilistically extracting Bell pairs from W states is more advantageous than deterministically extracting them from GHZ-like states in lossy networks, with this advantage increasing with network size. We further extend our analysis analytically, proving that W states remain more effective in large-scale networks. These findings offer valuable insights into the practical deployment of near-term networks, revealing a fundamental trade-off between deterministic entanglement distribution protocols and loss-sensitive resources.