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.

We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations. Introduction.-One-way quantum computation [1] provides the ability to perform universal quantum computation (QC) using only single-qubit projective measurements, given a specially prepared and highly entangled cluster state. This is in contrast to the traditional circuit model, where unitary evolution and coherent control of individual qubits are required [2]. Apart from its conceptual importance, the cluster-state approach can also lead to practical advantages. For example, the resources required for QC using linear optics [3] can be significantly reduced by first creating photonic cluster states via nondeterministic gates [4 -6]. Recently, a four-qubit cluster state has been demonstrated optically in the single-photon regime [7].While qubits are typically used in QC, Lloyd and Braunstein [8] proposed the use of continuous variables for QC and proved that only a finite set of continuousvariable (CV) gates are needed for universal QC. In the CV approach, the continuous degree of freedom may be used directly or lower-dimensional systems may be encoded within the modes, such as in the Gottesman-KitaevPreskill (GKP) proposal [9], which encodes one qubit into each mode. This allows, for instance, for the application of standard qubit protocols to CV systems. The optical modes of the electromagnetic field provide an experimental test bed for these ideas [10].In this Letter, we describe a model of universal QC using CV cluster states. We also propose an optical implementation of our scheme where squeezed-light sources serve as the nodes of the cluster. The main advantage of this approach is that not only can computations with the cluster be performed deterministically, but also the preparation of the cluster state, including connecting the nodes, can be done unconditionally. This is in contrast to the discrete-variable linear-optics schemes [4,6,11], where cluster states are created probabilistically. Therefore, the CV approach appears to be particularly suited for further experimental demonstration of the general principles of cluster-state QC.

Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states

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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We propose a new coherent state quantum key distribution protocol that eliminates the need to randomly switch between measurement bases. This protocol provides significantly higher secret key rates with increased bandwidths than previous schemes that only make single quadrature measurements. It also offers the further advantage of simplicity compared to all previous protocols which, to date, have relied on switching.

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.

Quantum illumination is a quantum-optical sensing technique in which an entangled source is exploited to improve the detection of a low-reflectivity object that is immersed in a bright thermal background. Here, we describe and analyze a system for applying this technique at microwave frequencies, a more appropriate spectral region for target detection than the optical, due to the naturally occurring bright thermal background in the microwave regime. We use an electro-optomechanical converter to entangle microwave signal and optical idler fields, with the former being sent to probe the target region and the latter being retained at the source. The microwave radiation collected from the target region is then phase conjugated and upconverted into an optical field that is combined with the retained idler in a joint-detection quantum measurement. The error probability of this microwave quantum-illumination system, or quantum radar, is shown to be superior to that of any classical microwave radar of equal transmitted energy.