  The wave-particle duality of light has led to two different encodings for
optical quantum information processing. Several approaches have emerged based
either on particle-like discrete-variable states, e.g. finite-dimensional
quantum systems, or on wave-like continuous-variable states, e.g.
infinite-dimensional systems. Here, we demonstrate the first
measurement-induced generation of entanglement between optical qubits of these
different types, located at distant places and connected by a lossy channel.
Such hybrid entanglement, which is a key resource for a variety of recently
proposed schemes, including quantum cryptography and computing, enables to
convert information from one Hilbert space to the other via teleportation and
therefore connect remote quantum processors based upon different encodings.
Beyond its fundamental significance for the exploration of entanglement and its
possible instantiations, our optical circuit opens the promises for
heterogeneous network implementations, where discrete and continuous-variable
operations and techniques can be efficiently combined.
