Radar technology has been a staple technology of both military and civilian sectors for decades, with its first conception in the late 1800s. The basic principle relies on reflecting a beam of electromagnetic radiation off of a target and measuring the received signal cross section, called the radar cross section (RCS). Measurement of the received and transmitted power, along with the RCS, informs the user on the range of the unknown entity. Recent investigation into quantum information, computing, and other applications have spurred an interest in using the properties of quantum mechanics to generate a higher fidelity radar system, potentially rendering classical radar technology obsolete. As a result, quantum radar has been actively investigated over the last decade. Quantum radar relies on the mutual information inherent in quantumly entangled photons to discern reflected signal photons from background noise, after which conventional radar signal processing techniques may be applied. In this paper, investigation into the theoretical feasibility of this technology is conducted via examining the detection probability of a quantum radar system juxtaposed to its classical counterparts. Additionally, the full derivation of the quantum radar cross section (QRCS) is carried out with the express purpose of direct comparison to the classical radar cross section (CRCS). The QRCS and CRCS is then manipulated in order to analytically observe a target of simple geometry (rectangular plate). Numerical analysis and plotting is provided, with Python source code. This work notes a stark difference between the response of the QRCS and the CRCS, with as much as two orders of magnitude larger observed cross section for the QRCS as compared to the CRCS. Detection probability is equally as promising, with a much higher detection probability in the sensing region where the signal to noise ratio (SNR) ≈ 1.