The radar cross section sigma(C) is an objective measure of the "radar visibility" of an object. As such, sigma(C) is an important concept for the correct characterization of the operational performance of radar systems. Furthermore, sigma(C) is equally essential for the design and development of stealth weapon systems and platforms. Recent years have seen the theoretical development of quantum radars, that is, radars that operate with a small number of photons. In this regime, the radar-target interaction is described through photon-atom scattering processes governed by the laws of quantum electrodynamics. As such, it is theoretically inconsistent to use the same sigma(C) to characterize the performance of a quantum radar. In this paper we define a quantum radar cross section sigma(Q) based on quantum electrodynamics and interferometric considerations. We discuss the theoretical challenges of defining sigma(Q), as well as computer simulations of sigma(C) and sigma(Q) for simple targets.