There are few experiments aiming at determining directly the mass of the electron antineutrino with a sensitivity of 0.2 eV by analyzing the end of theβ-decay spectrum of specific nuclei. This sensitivity can be only reached if the uncertainties arising from systematic effects are very small and very well determined. The same holds for experiments aiming at improving the sensitivity in the determination of the mass of the electron neutrino using electron-capture (ϵ)-decaying nuclei. One important input in these cases is an accurateQ-value of the decay which can be unambiguously determined from the difference of the mass of the mother and the daughter nuclei by means of Penning traps. In order to reach the required sensitivity, a novel device calledQuantum Sensoris under construction at the University of Granada (Spain). The device will allow measuring atomic masses, and thereforeQ-values from decays with unprecedented accuracy and sensitivity, using fluorescence photons from a laser-cooled ion instead of electronic detection. This paper will give an overview onQ-value measurements performed with Penning traps, relevant for neutrino mass spectrometry, describing the Quantum Sensor and the facility under construction. It will end by presenting the status of the project.