= APPENDIX: QUANTUM BASED TECHNOLOGIES =

### A. QUANTUM IMAGING

#### LANDMARK RESULTS

The aim of Quantum Imaging is to demonstrate that one can take advantage at the same time of the quantum mechanical aspects of light and of the fundamental and intrinsic parallelism of optical signals to develop new techniques in the processing of information at the quantum level. This kind of study is a rather new subject of quantum optics, and is in its infancy for most of its aspects. The first step was to produce, characterize, and implement first uses of spatially entangled non-classical light. Landmarks results obtained so far in Europe are the following:

The "quantum laser pointer": it has been experimentally demonstrated that it was possible to improve the measurement of the position of the center of a light beam at the Angstrom level, beyond the shot noise limit, in the two directions of the image plane.

Observation of a spatial quantum correlation in parametric down conversion: the intensity difference measured on symmetric pixels of the signal and idler images produced by pulsed parametric down-conversion in the macroscopic regime has been shown to be below the photon noise limit. Let us stress that the observed quantum effect is a pure spatial one, and not a temporal one, as was obtained by all previous experiments.

Observation of noiseless image parametric amplification: the pixel to pixel fluctuations in an image have been shown to be less degraded by the phase-sensitive pulsed parametric amplification than if one would have used a classical amplifier of the same gain. Here also, it is an effect measured on spatial averages, and not on spatially resolved temporal fluctuations.

Precise assignment of classical and quantum features in "two-photon imaging": this paradoxical technique allows one to obtain the image of an object by recording all the light that it scatters, and not its spatial distribution, provided that the measurement is made in coincidence with a spatially resolved measurement performed on a second light beam correlated with the first one. It turns out that it is essentially an effect related to classical spatial correlations.

#### VISIONS, PROSPECTS, CHALLENGES AND ROADBLOCKS

First important results have been obtained, and a worldwide community exists now on the subject. A lot of research work remains indeed to be done, on the experimental side, to improve the quality of the production of spatial entanglement both in the continuous wave and in the pulsed regime, but also on the theoretical side, to find more practical applications of spatial entanglement to information technologies. A promising alley of research is certainly the use of orbital angular momentum of light to convey and process quantum information.

#### HOW EACH AREA RELATES TO THE OTHERS AND TO THE GLOBAL PICTURE?

So far, the spatial quantum effects are somewhat on the edges of quantum computing, as they have been essentially used in the domain of metrology and information storage. No proposition has been made up to now to use the parallelism of optical imaging in quantum computing algorithms. This alley of research is undoubtedly interesting and requires collaborative work between the quantum computing and quantum imaging communities.

#### A.4 POTENTIAL APPLICATIONS

Microscopy, wavefront correction, image processing, optical data storage and optical measurements in general constitute a very important domain of our present day technologies. They can benefit in various ways from the researches on quantum imaging and quantum optics in general. At a first level, they can directly use the improvements brought by quantum effects and demonstrated by laboratory experiments, even though their complexity is an obstacle to such applications. At a less ambitious level, but perhaps more realistic, many optical technologies could be significantly improved by using the highly sophisticated methods developed in quantum optics labs to reach the level of quantum noise.