Nicolas Gisin * and Rob Thew

Quantum communication is the art of transferring a quantum state from one place to another. Traditionally, the sender is named Alice and the receiver Bob. Th e basic motivation is that quantum states code quantum information — called qubits in the case of two-dimensional Hilbert spaces — and that quantum information allows tasks to be performed that could only be achieved far less effi ciently, if at all, using classical information. Th e best known example is quantum key distribution (QKD)1–3. In fact, there is another motivation, at least equally important to most physicists, namely the close connection between quantum communication and quantum non-locality4,5, as illustrated by the fascinating process of quantum teleportation6. Quantum-communication theory is a broad fi eld, including for example, communication complexity7 and quantum bit-string commitment8 . In this review we restrict ourselves to its most promising application, QKD, both point to point and in futuristic networks. Th ere are several ways to realize quantum communication. We list them below from the simplest to the more involved. As ‘fl ying qubits’ are naturally realized by photons, we oft en use ‘photon’ to mean ‘quantum system’, although in principle, any other quantum system could do the job. Th e basic procedure is as follows. Alice encodes the state she wants to communicate into a quantum system and sends it to Bob. Entanglement is exploited to prepare the desired quantum state at a distance. Th e quantum state is then teleported from Alice to Bob and the entanglement is also teleported — entanglement swapping. In this review, a more intuitive perspective of quantum communication, overlooking this complexity, will be considered fi rst, starting from the basic ingredient, namely entanglement and its non-locality, continuing with weak-laser-pulse QKD and its security, before discussing quantum teleportation. Finally, a review of quantum relays as well as repeaters that require quantum memories will be given. Future challenges will be underlined throughout.