  We experimentally demonstrate that the nonlocal nature of time-bin entangled
photonic qubits persists when one or two qubits of the pair are converted to
polarization qubits. This is possible by implementing a novel Universal
Time-Bin Qubit Analyzer (UTBA), which, for the first time, allows analyzing
time-bin qubits in any basis. We reveal the nonlocal nature of the emitted
light by violating the Clauser-Horne-Shimony-Holt inequality with measurement
bases exploring all the dimensions of the Bloch sphere. Moreover, we conducted
experiments where one qubit is transmitted over a 12.4 km underground fiber
link and demonstrate the suitability of our scheme for use in a real-world
setting. The resulting entanglement can also be interpreted as hybrid
entanglement between different types of degrees of freedom of two physical
systems, which could prove useful in large scale, heterogeneous quantum
networks. This work opens new possibilities for testing nonlocality and for
implementing new quantum communication protocols with time-bin entanglement.
