The STE-QUEST M4 proposal

We summarise the Space-Time Explorer and QUantum Equivalence Space Test (STE-QUEST) space mission, as proposed to ESA in 2015 in response to the Cosmic Vision M4 call. STE-QUEST carries out tests of di�erent aspects of the Einstein Equivalence Principle using atomic clocks, matter wave interferometry, and long distance time/frequency links. We emphasize the speci�c strong interest of performing equivalence principle tests in the quantum regime, i.e. using quantum atomic wave interferometry. Although STE-QUEST was not selected in M4 because of budgetary and technological reasons, we are looking forward to future opportunities with hopefully better outcomes for the fascinating science of STE-QUEST at the Interface between quantum mechanics and gravitation.