  Quantum correlations are at the core of the power of quantum information and
are necessary to reach a quantum computational advantage. In the context of
continuous-variable quantum systems, another necessary ressource for quantum
advantages is non-Gaussianity. In this work, we propose a witness, based on
previously known relations between metrological power and quantum correlations,
to detect a strong form of entanglement that only non-Gaussian states possess
and that cannot be undone by passive optical operations, i.e., entanglement in
all mode bases. The strength of our witness is two-fold: it only requires
measurements in one basis to check entanglement in any arbitrary mode basis; it
can be made applicable experimentally using homodyne measurements and without
requiring a full tomography of the state.
