We report a proof-of-principle experimental demonstration of quantum lithography. Utilizing the entangled nature of a twophoton state, the experimental results have bettered the classical diffraction limit by a factor of two. This is a quantum mechanical two-photon phenomenon but not a violation of the uncertainty principle.

We report the first experimental demonstration of two-photon imaging with a pseudothermal source. Similarly to the case of entangled states, a two-photon Gaussian thin lens equation is observed, indicating EPR type correlation in position. We introduce the concepts of two-photon coherent and two-photon incoherent imaging. The differences between the entangled and the thermal cases are explained in terms of these concepts.

We report a quantum interference and imaging experiment which quantitatively demonstrates that Einstein-Podolsky-Rosen (EPR) type entangled two-photon states exhibit both momentummomentum and position-position correlations, stronger than any classical correlation. The measurements show indeed that the uncertainties in the sum of momenta and in the difference of positions of the entangled two-photon satisfy both EPR inequalities ∆(k1 + k2) < min(∆k1, ∆k2) and ∆(x1 − x2) < min(∆x1, ∆x2). These two inequalities, together, represent a non-classicality condition. Our measurements provide a direct way to distinguish between quantum entanglement and classical correlation in continuous variables for two-photons/two photons systems. The concept of multi-particle quantum entanglement, one of the most surprising consequences of quantum mechanics, was introduced in the very early days of quantum theory [1,2]. Since the development of spontaneous parametric down-conversion (SPDC) as an efficient source of two-photon entangled states in late 1980's [3], many experiments have been realized to exhibit and, afterwards, to exploit the very surprising quantum effects of entangled states for secure communication, information processing, and metrology applications [4].Some of the most intriguing effects of two-photon entanglement in SPDC are quantum 'ghost' interference and imaging [5,6]. These effects are of great importance in potential applications like quantum metrology and lithography [7,8,9]. Recently, it has been claimed that the two-photon 'ghost' image can be achieved using a pair of classically k-vector correlated optical pulses [10]. Ref.[10], therefore, raises interesting questions about fundamental issues of quantum theory, namely: (i) to what extent can quantum entanglement in continuous variables be simulated with classically correlated systems? and (ii) can we experimentally make a distinction between them?In this Letter, we report an experiment which sheds light on these two tightly related questions. Our idea is to exploit quantum interference-imaging effects to verify experimentally the EPR-type inequalities, which allow distinguishing quantum entanglement from classical correlation in continuous variables, for two-photon systems. By analyzing the results of a two-photon interference and imaging experiment, we show quantitatively that entangled two-photon pairs exhibit both momentum- *

Since the early days of quantum mechanics, physicists have been puzzled by the counterintuitive consequences of entanglement. Quantum imaging is one of the most intriguing effects exhibiting the typical nonlocal behavior of entangled states and has in fact stimulated an intense debate regarding fundamental issues of quantum theory. Recently, particular attention has been given to the possibility of simulating quantum imaging classically, that is, without entanglement. The study of quantum imaging has also lead to useful practical applications such as high precision nonlocal timing-positioning and quantum lithography, in which measurements may achieve resolution even beyond the classical limits. In this paper, we first introduce the concept of quantum imaging and emphasize its peculiar quantum nature through a set of inequalities derived from the historical argument of Einstein, Podolsky and Rosen (EPR). The EPR inequalities are the quantitative formulation of the very different physics governing entangled and separable systems. We show that twophoton imaging may achieve its fundamental limit only through nonlocal measurements realized on entangled photon pairs. Furthermore, we show that quantum imaging may be exploited to overcome the Rayleigh diffraction limit; this is the basic idea behind quantum lithography. Finally, we discuss the possibility of extending the coherent two-photon imaging typical of entangled photon pairs to incoherent coincidence imaging, by employing chaotic light. From an applicative viewpoint, chaotic radiation may represent the ideal candidate for mimicking quantum ghost imaging, provided adequate detection schemes are developed.

The quantum ghost imaging phenomena, experimentally demonstrated a decade ago, exploited the apparent spooky action at a distance of entangled photon pairs and offered a novel approach toward imaging. Can ghost imaging effects be produced by "classical" light sources, such as separable systems of photon pairs or thermal light? If so, can these sources achieve the same accuracy achieved by entangled states? In order to answer these questions, we formulate the different physics behind entangled and separable systems in terms of a set of inequalities derived from the historical argument of Einstein, Podolsky, and Rosen. We show that the ghost images produced by separable sources are subject to the standard statistical limitations. However, entangled states offer the possibility of overcoming such limitations. Imaging can, therefore, achieve its fundamental limit through the high spatial resolution and nonlocal behavior of entangled systems.