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.

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.

The classical capacity of the lossy bosonic channel is calculated exactly. It is shown that its Holevo information is not superadditive, and that a coherent-state encoding achieves capacity. The capacity of far-field, free-space optical communications is given as an example.PACS numbers: 03.67. Hk,89.70.+c,05.40.Ca A principal goal of quantum information theory is evaluating the information capacities of important communication channels. At present-despite the many efforts that have been devoted to this endeavor and the theoretical advances they have produced [1]-exact capacity results are known for only a handful of channels. In this paper we consider the lossy bosonic channel, and we develop an exact result for its classical capacity C, i.e., the number of bits that it can communicate reliably per channel use. The lossy bosonic channel consists of a collection of bosonic modes that lose energy en route from the transmitter to the receiver. Typical examples are free space or optical fiber transmission, in which photons are employed to convey the information. The classical capacity of the lossless bosonic channel-whose transmitted states arrive undisturbed at the receiver-was derived in [2,3]. When there is loss, however, the received state is in general different from the transmitted state, and quantum mechanics requires that there be an accompanying quantum noise source. In [4] a first step toward the capacity of such channels was given by considering only separable encoding procedures. Here, on the contrary, it is proven that the optimal encoding is indeed separable. We obtain the value of C in the presence of loss when the quantum noise source is in the vacuum state, i.e., when it injects the minimum amount of noise into the receiver. Our derivation proceeds by developing an upper bound for C and then showing that this bound coincides with the lower bound on C reported in [5,6]. Our upper bound results from comparing the capacity of the lossy channel to that of the lossless channel whose average input energy matches the average output energy constraint for the lossy case [7]. This argument is analogous to the derivation of the classical capacity of the erasure channel [8]. The lower bound comes from calculating the Holevo information for appropriately coded coherent-state inputs. Thus, because the two bounds coincide, we not only have the capacity of the lossy bosonic channel, but we also know that capacity can be achieved by transmitting coherent states.

Ghost-imaging experiments correlate the outputs from two photodetectors: a high spatialresolution (scanning pinhole or CCD camera) detector that measures a field which has not interacted with the object to be imaged, and a bucket (single-pixel) detector that collects a field that has interacted with the object. We describe a computational ghost-imaging arrangement that uses only a single-pixel detector. This configuration affords background-free imagery in the narrowband limit and a 3D sectioning capability. It clearly indicates the classical nature of ghost-image formation.

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.

By embedding an atom capable of electromagnetically induced transparency inside an appropriate photoniccrystal microcavity it may become possible to realize an optical nonlinearity that can impart a -rad-peak phase shift in response to a single-photon excitation. Such a device, if it operated at high fidelity, would then complete a universal gate set for all-optical quantum computation. It is shown here that the causal, noninstantaneous behavior of any ͑3͒ nonlinearity is enough to preclude such a high-fidelity operation. In particular, when a single-photon-sensitive ͑3͒ nonlinearity has a response time that is much shorter than the duration of the quantum computer's single-photon pulses, essentially no overall phase shift is imparted to these pulses by cross-phase modulation. Conversely, when this nonlinearity has a response time that is much longer than this pulse duration a single-photon pulse can induce a -rad overall phase shift through cross-phase modulation, but the phase noise injected by the causal, noninstantaneous response function precludes this from being a high-fidelity operation.

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