  Heterogeneous quantum networks consisting of mixed-technologies - Continuous
Variable (CV) and Discrete Variable (DV) - will become ubiquitous as global
quantum communication matures. Hybrid quantum-entanglement between CV and DV
modes will be a critical resource in such networks. A leading candidate for
such hybrid quantum entanglement is that between Schr\"odinger-cat states and
photon-number states. In this work, we explore the use of Two-Mode Squeezed
Vacuum (TMSV) states, distributed from satellites, as a teleportation resource
for the re-distribution of our candidate hybrid entanglement pre-stored within
terrestrial quantum networks. We determine the loss conditions under which
teleportation via the TMSV resource outperforms direct-satellite distribution
of the hybrid entanglement, in addition to quantifying the advantage of
teleporting the DV mode relative to the CV mode. Our detailed calculations show
that under the loss conditions anticipated from Low-Earth-Orbit, DV
teleportation via the TMSV resource will always provide for significantly
improved outcomes, relative to other means for distributing hybrid entanglement
within heterogeneous quantum networks.
