  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\%.
