We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties, Alice and Bob. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state superposition) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement imperfections, and the associated success probability of the measurement schemes chosen in this protocol.
    We show that our entanglement swapping scheme is resilient to low levels of photonic losses, as well as low levels of averaged unequal losses between the two propagating modes, and show an improvement in this loss resilience over other hybrid entanglement schemes using coherent state superpositions as the propagating modes. Finally, we conclude that our protocol is suitable for potential quantum networking applications which require two nodes to share entanglement separated over a distance of 5-10 km when used with a suitable entanglement purification scheme.

The dataset includes mathematica code to generate final density matrix of cat state entanglement swapping protocol, including averaged unequal photonic losses between both propagating modes. 

The fidelity plots, and success probability plots, can be generated using this code. 

Note that to run this code to reproduce the data as published in this manuscript, the "non-ideal" homodyne measurement variable (\epsilon) should be ignored. Therefore \epsilon should be set to 0 in the code. 

NB - the QDensity Mathematica package (available at: https://library.wolfram.com/infocenter/MathSource/5715/) is required to correctly run this code.