  Hybrid entanglement swapping supports the teleportation of any arbitrary
states, regardless of whether the quantum information in the state is encoded
in Discrete Variables (DV) or Continuous Variables (CV). In this work, we study
the CV teleportation channel created between two ground receivers via direct
lossy-distribution from a low-Earth-orbit (LEO) satellite. Such a flexible
teleportation protocol has the potential to interconnect a global array of
quantum-enabled devices regardless of the different intrinsic technology upon
which the devices are built.
  However, past studies of hybrid entanglement swapping have not accounted for
channel transmission loss. Here we derive the general framework for teleporting
an arbitrary input mode over a lossy CV teleportation channel. We investigate
the specific case where the input modes are part of DV states entangled in the
photon number basis, then identify the optimal teleportation strategy.
  Our results show that, relative to DV photon-number entanglement sourced
directly from the satellite, there are circumstances where our teleported DV
states retain higher entanglement quality. We discuss the implications of our
new results in the context of generating a global network of ultra-secure
communications between different quantum-enabled devices which possess
line-of-sight connections to LEO satellites. Specifically, we illustrate the
impact the teleportation process has on the key rates from a Quantum Key
Distribution protocol.
