Identifying Entanglement Using Quantum Ghost Interference and Imaging

Abstract

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- *

Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis

“…Therefore, to identify the difference between the pattern produced by quantum correlated photons and that by classically correlated beams in the case of ghost interference experiments, more detailed discussion is required as reported in Ref. [28,29]. On the other hand, the difference clearly appears in the case of the experiment in which two photons pass through the same object, that is, R (1) A (q) = R (1) B (q) in Eq.…”

“…11(b)). Recently, several groups have reported coincidence imaging experiments using classical light sources, which stimulated discussion regarding the difference between quantum and classical coincidence imaging [21,27,28,29,30]. Two types of experiment use classical light sources.…”

Scheme for directly observing the noncommutativity of the position and the momentum operators with interference

“…[5] and demonstrated in Ref. [14,15]. The position-momentum uncertainty relation can be in-vestigated with the single-slit diffraction experiment involving a quantum object [12,13] and it has been demonstrated experimentally for neutrons [16] and for large fullerene molecules [17].…”

Einstein-Podolsky-Rosen Entanglement of Narrow-Band Photons from Cold Atoms

“…Genuine EPR position-momentum entanglement of photon pairs became available later by the SPDC process in a bulk crystal [14,15] and is thought to be essential in quantum imaging and quantum metrology [16][17][18][19]. The EPR-entangled SPDC photons, however, are inherently broadband, typically on the order of several THz in bandwidth.…”

“…The gedankenexperiment proposed by Einstein-Podolsky-Rosen (EPR) in 1935, on the other hand, involves a pair of particles that are entangled in their positions and momenta [13][14][15]. In addition to fundamental interests, EPR entanglement is essential in quantum imaging and quantum metrology [16][17][18][19].…”