In recent years, light field technology has attracted the interest of academia and industry, thanks to the possibility of rendering 3D scenes in a more realistic and immersive way. In particular, light field displays have been consistently investigated for their ability to offer a glass-free 3D viewing experience. Among others, tensor displays represent a promising way to render light field contents. However, only a few prototypes of such type of displays have been implemented and are available to the scientific community. As a direct consequence, the visual quality of such displays has not been rigorously investigated. In this paper, we propose a new framework to assess the visual quality of light field tensor displays on conventional 2D screens. The multilayer components of the tensor displays are virtually rendered on a typical 2D monitor through the use of a GUI, and different viewing angles can be accessed by simple mouse interactions. Both single and double stimulus methodologies for subjective quality assessment of light field contents are supported in this framework, while the total time of interaction is recorded for every stimulus. Results obtained in two different laboratory settings demonstrate that the framework can be successfully used to perform subjective quality assessment of different compression solutions for light field tensor displays.