The emergence of quantum technologies, including cold atom based accelerometers, offers an opportunity to improve the performances of space geodesy missions. In this context, CNES initiated an assessment study called GRICE (GRadiom\'etrie \`a Interf\'erom\`etres quantiques Corr\'el\'es pour l'Espace) in order to evaluate the contribution of cold atom technologies to space geodesy and to the end users of geodetic data. In this paper, we present mission scenario for gravity field mapping based on a long baseline gradiometer. The mission is based on a constellation of two satellites, flying at an altitude of 373 km, each equipped with a cold atom accelerometer with a sensitivity of $6 \times 10^{-10}$~m.s$^{-2}$.$\mathrm{\tau}^{-1/2}$. A laser link measures the distance between the two satellites and couples these two instruments in order to produce a correlated differential acceleration measurement. The main parameters, determining the performances of the payload, have been investigated. We carried out a general study of satellite architecture and simulations of the mission performances in terms of restitution of the gravity field. The simulations show that this concept would give its best performance in terms of monthly gravity fields recovery under 1000~km resolution. In the resolution band between 1000 and 222~km, the improvement of the GRICE gradient approach over the traditional range-rate approach is globally in the order of 10 to 25\%.