  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.
