Fidelity and efficiency analysis for heralded entanglement swapping in lossy channels: linear and nonlinear optical approaches

Bell state measurements (BSMs) of photonic qubits are used for quantum networking protocols to herald the distribution and transfer of quantum information. However, standard BSMs based on linear optics (LO-BSMs) require identical photons and are susceptible to errors from multiphoton emissions, leading to reduced fidelity of protocols, particularly in the absence of postselection. To overcome these challenges, Bell state measurements based on nonlinear optics (NLO-BSMs) have been proposed and implemented, leveraging sum-frequency generation (SFG) to filter out multiphoton emissions and improve the fidelity without postselection. Here we analyze the fidelity of LO-BSM and NLO-BSM heralded entanglement swapping in lossy channels and compare their performance under realistic conditions. We also explore the impact of state-of-the-art nonlinear photonics platforms on SFG efficiency and highlight how advances in nanophotonics will enable practical, high-fidelity NLO-BSM-based quantum networking applications.