Resolution of quantum and classical ghost imaging

Milena D’Angelo, Alejandra Valencia, Morton H. Rubin, and Yanhua Shih

Phys. Rev. A 72, 013810 – Published 14 July 2005

Abstract

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.

Received 15 September 2004

DOI:https://doi.org/10.1103/PhysRevA.72.013810

Authors & Affiliations

Milena D’Angelo^*, Alejandra Valencia, Morton H. Rubin, and Yanhua Shih

Department of Physics, University of Maryland at Baltimore County, Baltimore, Maryland 21250, USA

^*Electronic address: dmilena1@umbc.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 72, Iss. 1 — July 2005

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(Color online) (a) A lens produces the stigmatic image of an object in the plane defined by the Gaussian thin-lens equation $1 ∕ s_{i} + 1 ∕ s_{o} = 1 ∕ f$ . The concept of image is based on the existence of a point-to-point relationship between the object plane and the image plane. (b) A light source illuminates an object and no image forming system is present; no image plane is defined: only projections, or shadows, of the object can be observed.Reuse & Permissions
Figure 2
(Color online) Schematic setup to observe a quantum ghost image. The source emits a pair of photons in all possible directions but their momenta are always equal and opposite (note the arrows on the “straight lines”). Object and imaging lens are inserted on one side of the source; a ghost image appears when counting coincidences between the fix bucket detector $D_{1}$ and the scanning pointlike detector $D_{2}$ . The image plane is defined by the two-photon thin-lens equation $1 ∕ S_{i} + 1 ∕ S_{o} = 1 ∕ f$ .Reuse & Permissions
Figure 3
Pictorial representation of the inequalities of Eqs. (3, 8), characterizing, respectively, entangled (shaded rectangle) and separable (dotted square) systems of two quanta. The dimensions of the squares in position and momentum spaces are related to each other by the uncertainty relation $Δ p_{1, 2} = ℏ ∕ (2 Δ x_{1, 2})$ , while the dimensions of the shaded rectangles are related by the uncertainty relations $Δ (p_{1} + p_{2}) = ℏ ∕ Δ (x_{1} + x_{2})$ and $Δ (p_{1} - p_{2}) = ℏ ∕ Δ (x_{1} - x_{2})$ [Eqs. (6)].Reuse & Permissions
Figure 4
(Color online) Schematic of the setup for implementing EPR correlation measurements on optical sources. The source emits pairs of photons in all possible directions, but always with opposite momenta. The system of photons can either be entangled or separable. For practical implementations, one should consider the folded version of this setup.Reuse & Permissions
Figure 5
(Color online) The source emits pairs of photons in a classical statistical mixture that simulates the SPDC entangled two-photon system. The average momenta (dashed lines) of photons 2 intersect in the plane at distance $s_{i}$ from the lens, but the spread in the momenta of photons 2 (diverging continuous lines) is such that no image plane can be defined neither theoretically nor experimentally. Only projections (shaded arrows) can be observed. Also notice that, due to the dimensions of the single-photon beams compared to the object size, this source does not allow reproducing the Fourier transform of the object.Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information