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Conference on Lasers and Electro-Optics

Identifying entanglement using quantum "ghost" interference and imaging

Milena D’Angelo, Yoon-Ho Kim, S. P. Kulik, Yanhua H. Shih

Published Jan 1, 2004• 16 citations
Publisher

Abstract

We report a quantum interference and imaging experiment which shows quantitatively that entangled two-photon violate the EPR inequality. This measurement provides a direct way to distinguish quantum entanglement from classical correlation in continuous variables.
DOI
10.1364/iqec.2004.itum2

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We report a quantum interference and imaging experiment which allows identifying the entanglement in momentum and position variables of a two-photon system. 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 $\ensuremath{\Delta}({k}_{1}+{k}_{2})<\mathrm{min}(\ensuremath{\Delta}{k}_{1},\ensuremath{\Delta}{k}_{2})$ and $\ensuremath{\Delta}({x}_{1}\ensuremath{-}{x}_{2})<\mathrm{min}(\ensuremath{\Delta}{x}_{1},\ensuremath{\Delta}{x}_{2})$. These two inequalities, together, represent a nonclassicality condition. Our measurements provide a direct way to distinguish between quantum entanglement and classical correlation in continuous variables for systems of pairs of photons.

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We report a quantum interference and imaging experiment which allows identifying the entanglement in momentum and position variables of a two-photon system. 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 $\ensuremath{\Delta}({k}_{1}+{k}_{2})<\mathrm{min}(\ensuremath{\Delta}{k}_{1},\ensuremath{\Delta}{k}_{2})$ and $\ensuremath{\Delta}({x}_{1}\ensuremath{-}{x}_{2})<\mathrm{min}(\ensuremath{\Delta}{x}_{1},\ensuremath{\Delta}{x}_{2})$. These two inequalities, together, represent a nonclassicality condition. Our measurements provide a direct way to distinguish between quantum entanglement and classical correlation in continuous variables for systems of pairs of photons.
Although questions regarding fundamental issues of quantum theory still exist, quantum entanglement has started to play important roles in practical engineering applications. Quantum imaging is one of these exciting areas. Quantum imaging has so far demonstrated three peculiar features: enhancing the spatial resolution of imaging beyond the diffraction limit; reproducing ghost images in a “nonlocal” manner; and dispersion-cancelation or turbulence-free imaging. The enhanced spatial resolution apparently “violates” the uncertainty principle. The ghost imaging is considered as a “nonlocal” phenomenon due to a point-to-point correlation of two interaction-free photons at distance. All the peculiar features are the results of two-photon interference, which involves the superposition of two-photon amplitudes, a nonclassical entity corresponding to different yet indistinguishable alternative ways of creating a joint-detection event. The effect of turbulence on a classic image can be easily seen from the blurring of the images.
One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. In an entangled EPR two-particle system, the value of the momentum (position) for neither single subsystem is determined. However, if one of the subsystems is measured to have a certain momentum (position), the other subsystem is determined to have a unique corresponding value, despite the distance between them. This peculiar behavior of an entangled quantum system has surprisingly been observed experimentally in two-photon temporal and spatial correlation measurements, such as ghost interference and ghost imaging. This article addresses the fundamental concerns behind these experimental observations and to explore the nonclassical nature of two-photon superposition by emphasizing the physics of 2 is not 1 + 1.
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 two-photon 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.