  Robust implementation of quantum key distribution requires precise state
generation and measurements, as well as a transmission that is resistant to
channel disturbances. However, the choice of the optimal encoding scheme is not
trivial and depends on external factors such as the quantum channel. In fact,
stable and low-error encoders are available for polarization encoding, suitable
for free-space channels, whereas time-bin encoding represent a good candidate
for fiber-optic channels, as birefingence does not perturb this kind of states.
Here we present a cross-encoded scheme where high accuracy quantum states are
prepared through a self-compensating, calibration-free polarization modulator
and transmitted using a polarization-to-time-bin converter. A hybrid receiver
performs both time-of-arrival and polarization measurements to decode the
quantum states and successfully leaded to a transmission over 50 km fiber spool
without disturbances. Temporal synchronization between the two parties is
performed with a qubit-based method that does not require additional hardware
to share a clock reference. The system was tested in a 12 hour run and
demonstrated good and stable performance in terms of key and quantum bit error
rates. The flexibility of our approach represents an important step towards the
development of hybrid networks with both fiber-optic and free-space links.
