  Genuine multipartite entanglement represents the strongest type of
entanglement, which is an essential resource for quantum information
processing. Standard methods to detect genuine multipartite entanglement, e.g.,
entanglement witnesses, state tomography, or quantum state verification,
require full knowledge of the Hilbert space dimension and precise calibration
of measurement devices, which are usually difficult to acquire in an
experiment. The most radical way to overcome these problems is to detect
entanglement solely based on the Bell-like correlations of measurement outcomes
collected in the experiment, namely, device-independently (DI). However, it is
difficult to certify genuine entanglement of practical multipartite states in
this way, and even more difficult to quantify it, due to the difficulty to
identify optimal multipartite Bell inequalities and protocols tolerant to state
impurity. In this work, we explore a general and robust DI method which can be
applied to various realistic multipartite quantum state in arbitrary finite
dimension, while merely relying on bipartite Bell inequalities. Our method
allows us both to certify the presence of genuine multipartite entanglement and
to quantify it. Several important classes of entangled states are tested with
this method, leading to the detection of genuinely entangled states. We also
certify genuine multipartite entanglement in weakly-entangled GHZ states, thus
showing that the method applies equally well to less standard states.
