  Generalised parton distributions are instrumental to study both the
three-dimensional structure and the energy-momentum tensor of the nucleon, and
motivate numerous experimental programmes involving hard exclusive
measurements. Based on a next-to-leading order analysis and a careful study of
evolution effects, we exhibit non-trivial generalised parton distributions with
arbitrarily small imprints on deeply virtual Compton scattering observables.
This means that in practice the reconstruction of generalised parton
distributions from measurements, known as the deconvolution problem, does not
possess a unique solution for this channel. In this Letter we discuss the
consequences on the extraction of generalised parton distributions from data
and advocate for a multi-channel analysis.
