Equivalence of Classical and Quantum Electromagnetic Scattering in the Far-Field Regime

Quantum remote sensing, also known as quantum detection and ranging (QUDAR), is the use of entangled photon states to detect targets at a stand-off distance. It inherently relies on sending many single photons through free space, bouncing off of a target and returning to the sensor. It is therefore necessary to understand how single photons interact and scatter from targets of macroscopic size. This article relates quantum and classical scattering in the far-field regime. Specifically, we show that due to the photon's position uncertainty, the path over which the photon traverses is not well defined, and this causes quantum interference. The result of this interference exactly replicates classical scattering behavior of electromagnetic waves. We will show that one can exactly derive the classical electric field scattering integral using a purely quantum construction. Although this article focuses on the context of QUDAR, it is very general to any application involving far-field electromagnetic scattering. Finally, we delve into the QUDAR multiphoton quantum scattering advantage shown in previous literature and further develop the theory. Specifically, we provide explanations as to why this advantage has not been observed in the classical regime, as well as provide insight as to the experimental requirements necessary to achieve this cross-section enhancement.