Quantum field theory and inverse problems: Imaging with Entangled Photons

TL;DR

This paper demonstrates that quantum field theory combined with entangled photon measurements enables unique imaging of atomic densities through inverse problem techniques involving nonlocal PDEs.

Contribution

It introduces a novel approach linking quantum field theory, entangled photon measurements, and inverse problems for imaging atomic densities.

Findings

Unique determination of atomic density from photon correlation measurements.

Use of nonlocal PDEs to model photon scattering and imaging.

Exploitation of photon entanglement for improved inverse problem solutions.

Abstract

We consider the quantum field theory for a scalar model of the electromagnetic field interacting with a system of two-level atoms. In this setting, we show that it is possible to uniquely determine the density of atoms from measurements of the source to solution map for a system of nonlocal partial differential equations, which describe the scattering of a two-photon state from the atoms. The required measurements involve correlating the outputs of a point detector with an integrating detector, thereby exploiting information about the entanglement of the photons.