The precise navigation of underwater vehicles is a difficult task due to the challenges imposed by the variable oceanic environment. It is particularly difficult if the underwater vehicle is trying to navigate under the Arctic ice shelf. Indeed, in this scenario traditional navigation devices such as GPS, compasses and gyrocompasses are unavailable or unreliable. In addition, the shape and thickness of the ice shelf is variable throughout the year. Current Arctic underwater navigation systems include sonar arrays to detect the proximity to the ice. However, these systems are undesirable in a wartime environment, as the sound gives away the position of the underwater vehicle. In this paper we briefly describe the theoretical design of a quantum imaging system that could allow the safe and stealthy navigation of underwater Arctic vehicles.