  Distributing quantum entanglement on a chip is a crucial step towards
realizing scalable quantum processors. Using traveling phonons - quantized
guided mechanical wavepackets - as a medium to transmit quantum states is
currently gaining significant attention, due to their small size and low
propagation speed compared to other carriers, such as electrons or photons.
Moreover, phonons are highly promising candidates to connect heterogeneous
quantum systems on a chip, such as microwave and optical photons for
long-distance transmission of quantum states via optical fibers. Here, we
experimentally demonstrate the feasibility of distributing quantum information
using phonons, by realizing quantum entanglement between two traveling phonons
and creating a time-bin encoded traveling phononic qubit. The mechanical
quantum state is generated in an optomechanical cavity and then launched into a
phononic waveguide in which it propagates for around two hundred micrometers.
We further show how the phononic, together with a photonic qubit, can be used
to violate a Bell-type inequality.
