The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

Quantum communications promises reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks, we need to determine the optimal point-to-point rates that are achievable by two remote parties at the ends of a quantum channel, without restrictions on their local operations and classical communication, which can be unlimited and two-way. These two-way assisted capacities represent the ultimate rates that are reachable without quantum repeaters. Here, by constructing an upper bound based on the relative entropy of entanglement and devising a dimension-independent technique dubbed ‘teleportation stretching', we establish these capacities for many fundamental channels, namely bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels in arbitrary dimension. In particular, we exactly determine the fundamental rate-loss tradeoff affecting any protocol of quantum key distribution. Our findings set the limits of point-to-point quantum communications and provide precise and general benchmarks for quantum repeaters.

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An optical transmitter irradiates a target region containing a bright thermal-noise bath in which a low-reflectivity object might be embedded. The light received from this region is used to decide whether the object is present or absent. The performance achieved using a coherent-state transmitter is compared with that of a quantum-illumination transmitter, i.e., one that employs the signal beam obtained from spontaneous parametric down-conversion. By making the optimum joint measurement on the light received from the target region together with the retained spontaneous parametric down-conversion idler beam, the quantum-illumination system realizes a 6 dB advantage in the error-probability exponent over the optimum reception coherent-state system. This advantage accrues despite there being no entanglement between the light collected from the target region and the retained idler beam.

Quantum teleportation is one of the most important protocols in quantum information. By exploiting the physical resource of entanglement, quantum teleportation serves as a key primitive in a variety of quantum information tasks and represents an important building block for quantum technologies, with a pivotal role in the continuing progress of quantum communication, quantum computing and quantum networks. Here we review the basic theoretical ideas behind quantum teleportation and its variant protocols. We focus on the main experiments, together with the technical advantages and disadvantages associated with the use of the various technologies, from photonic qubits and optical modes to atomic ensembles, trapped atoms, and solid-state systems. Analysing the current state-of-the-art, wefinish by discussing open issues, challenges and potential future implementations. From Science Fiction to RealityIt has been over two decades since the discovery of quantum teleportation, in what is arguably one of the most interesting and exciting implications of the 'weirdness' of quantum mechanics. Previous to this landmark discovery, this fascinating idea belonged to the realm of science fiction. First coined in a 1931 book by Charles H. Fort 1 , the term teleportation has since been used to refer to the process by which bodies and objects are transferred from one location to another, without actually making the journey along the way. Since then it has become a fixture of pop culture, perhaps best exemplified by Star Trek's celebrated catchphrase "Beam me up, Scotty."In 1993, a seminal paper 2 described a quantum information protocol, dubbed quantum teleportation, that shares several of the above features. In this protocol, an unknown quantum state of a physical system is measured and subsequently reconstructed or 'reassembled' at a remote location (the physical constituents of the original system remain at the sending location). This process requires classical communication and excludes superluminal communication. Most importantly, it requires the resource of quantum entanglement 3,4 . Indeed, quantum teleportation can be seen as the protocol in quantum information that most clearly demonstrates the character of quantum entanglement as a resource: Without its presence, such a quantum state transfer would not be possible within the laws of quantum mechanics.Quantum teleportation plays an active role in the progress of quantum information science [5][6][7][8] . On the one hand it is a conceptual protocol crucial in the development of formal quantum information theory, on the other it represents a fundamental ingredient to the development of many quantum technologies. Schemes such as quantum repeaters 9 -pivotal for quantum communication over large distances -quantum gate teleportation 10 , measurement-based computing 11 , and port-based teleportation 12 all derive from the basic scheme. The vision of a quantum network 13 draws inspiration from it. Teleportation has also been used as a simple tool for exploring 'extreme' physics,...

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Quantum key distribution (QKD) offers the promise of absolutely secure communications. However, proofs of absolute security often assume perfect implementation from theory to experiment. Thus, existing systems may be prone to insidious side-channel attacks that rely on flaws in experimental implementation. Here we replace all real channels with virtual channels in a QKD protocol, making the relevant detectors and settings inside private spaces inaccessible while simultaneously acting as a Hilbert space filter to eliminate side-channel attacks. By using a quantum memory we find that we are able to bound the secret-key rate below by the entanglement-distillation rate computed over the distributed states.

Quantum sensing has become a mature and broad field. It is generally related with the idea of using quantum resources to boost the performance of a number of practical tasks, including the radar-like detection of faint objects, the readout of information from optical memories or fragile physical systems, and the optical resolution of extremely close point-like sources. Here we first focus on the basic tools behind quantum sensing, discussing the most recent and general formulations for the problems of quantum parameter estimation and hypothesis testing. With this basic background in our hands, we then review emerging applications of quantum sensing in the photonic regime both from a theoretical and experimental point of view. Besides the state-of-the-art, we also discuss open problems and potential next steps.