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 discretevariable states, e.g. finite-dimensional quantum systems, or on wave-like continuous-variable states, e.g. infinite-dimensional systems. Here, we demonstrate the first 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.

Quantum memory for flying optical qubits is a key enabler for a wide range of applications in quantum information. A critical figure of merit is the overall storage and retrieval efficiency. So far, despite the recent achievements of efficient memories for light pulses, the storage of qubits has suffered from limited efficiency. Here we report on a quantum memory for polarization qubits that combines an average conditional fidelity above 99% and efficiency around 68%, thereby demonstrating a reversible qubit mapping where more information is retrieved than lost. The qubits are encoded with weak coherent states at the single-photon level and the memory is based on electromagnetically-induced transparency in an elongated laser-cooled ensemble of cesium atoms, spatially multiplexed for dual-rail storage. This implementation preserves high optical depth on both rails, without compromise between multiplexing and storage efficiency. Our work provides an efficient node for future tests of quantum network functionalities and advanced photonic circuits.