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arXiv:quant-ph/0612070

Ghost Imaging: What is quantum, what is not

Baris I. Erkmen, Jeffrey H. Shapiro

Published Dec 10, 2006• 4 citations
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Abstract

We provide a unified treatment of classical and quantum Gaussian-state sources that unambiguously identifies which features of ghost imaging are strictly quantum mechanical. We show that ghost-image formation is fundamentally classical, with the image being expressible in terms of the phase-insensitive and phase-sensitive cross correlations between the detected fields. We then consider ghost-imaging scenarios with either phase-insensitive or phase-sensitive sources, where the former are always classical but the latter may be classical or quantum mechanical. We show that if their auto-correlations are identical, then a quantum source provides resolution improvement in its near-field and field-of-view improvement in its far field when compared to a classical source.

DOI
10.48550/arxiv.quant-ph/0612070

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We provide a unified treatment of classical and quantum Gaussian-state sources that unambiguously identifies which features of ghost imaging are strictly quantum mechanical. We show that ghost-image formation is fundamentally classical, with the image being expressible in terms of the phase-insensitive and phase-sensitive cross correlations between the detected fields. We then consider ghost-imaging scenarios with either phase-insensitive or phase-sensitive sources, where the former are always classical but the latter may be classical or quantum mechanical. We show that if their auto-correlations are identical, then a quantum source provides resolution improvement in its near-field and field-of-view improvement in its far field when compared to a classical source.
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The theory of partial coherence has a long and storied history in classical statistical optics. The vast majority of this work addresses fields that are statistically stationary in time, hence their complex envelopes only have phase-insensitive correlations. The quantum optics of squeezed-state generation, however, depends on nonlinear interactions producing baseband field operators with phase-insensitive and phase-sensitive correlations. Utilizing quantum light to enhance imaging has been a topic of considerable current interest, much of it involving biphotons, i.e., streams of entangled-photon pairs. Biphotons have been employed for quantum versions of optical coherence tomography, ghost imaging, holography, and lithography. However, their seemingly quantum features have been mimicked with classical-state light, questioning wherein lies the classical-quantum boundary. We have shown, for the case of Gaussian-state light, that this boundary is intimately connected to the theory of phase-sensitive partial coherence. Here we present that theory, contrasting it with the familiar case of phase-insensitive partial coherence, and use it to elucidate the classical-quantum boundary of ghost imaging. We show, both theoretically and experimentally, that classical phase-sensitive light produces ghost images most closely mimicking those obtained with biphotons, and we derive the spatial resolution, image contrast, and signal-to-noise ratio of a standoff-sensing ghost imager, taking into account target-induced speckle.
In this letter, we use quantum description and the Gaussian state to study reflective ghost imaging with two classical sources, and to provide their expressions.We find that the reflective ghost imaging of a roughsurfaced object, using Gaussian-state phase-insensitive or classically correlated phase-sensitive light, can be expressed in terms of the phase-insensitive or phase-sensitive cross-correlations between the two detected fields, including a background term.Moreover, reflective ghost imaging with two classical Gaussian-state lights is shown to have similar features as spatial resolution and field of view.
In this letter,we use quantum description and the Gaussian state to study reflective ghost imaging with two classical sources,and to provide their expressions.We find that the reflective ghost imaging of a roughsurfaced object,using Gaussian-state phase-insensitive or classically correlated phase-sensitive light,can be expressed in terms of the phase-insensitive or phase-sensitive cross-correlations between the two detected fields,including a background term.Moreover,reflective ghost imaging with two classical Gaussian-state lights is shown to have similar features as spatial resolution and field of view.
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.