  Fiber-based quantum communication networks are currently limited without
quantum repeaters. Satellite-based quantum links have been proposed to extend
the network domain. We have developed a quantum communication system, suitable
for realistic satellite-to-ground communication. With this system, we have
executed an entanglement-based quantum key distribution (QKD) protocol
developed by Bennett, Brassard, and Mermin in 1992 (BBM92), achieving quantum
bit error rates (QBER) below 2$\%$ in all bases. More importantly, we
demonstrate low QBER execution of a higher dimensional hyperentanglement-based
QKD protocol, using photons simultaneously entangled in polarization and
time-bin, leading to significantly higher secure key rates, at the cost of
increased technical complexity and system size. We show that our protocol is
suitable for a space-to-ground link, after incorporating Doppler shift
compensation, and verify its security using a rigorous finite-key analysis.
Additionally, We discuss system engineering considerations relevant to those
and other quantum communication protocols, and their dependence on what
photonic degrees of freedom are utilized.
