  An open challenge in physics is to expand the frontiers of the validity of
quantum mechanics by evidencing nonclassicality of the centre of mass state of
a macroscopic object. Yet another equally important task is to evidence the
essential nonclassicality of the interactions which act between macroscopic
objects. Here we introduce a new tool to meet these challenges: massive spatial
qubits. In particular, we show that if two distinct localized states of a mass
are used as the $|0\rangle$ and $|1\rangle$ states of a qubit, then we can
measure this encoded spatial qubit with a high fidelity in the $\sigma_x,
\sigma_y$ and $\sigma_z$ bases simply by measuring its position after different
durations of free evolution. We show how this technique can be used to reveal
an irreducible nonclassicality through a Bell-inequality violation arising from
the entanglement of the centre of mass of a nano-crystal with its spin in a
Stern-Gerlach setup. Secondly, we show how our methodology, in conjuction with
the Casimir interaction, offers a powerful method to create and certify
non-Gaussian entanglement between two neutral nano-objects. Fundamentally, the
generation of such an entanglement provides an empirical means for
demonstrating an inherent quantumness of the Casimir interaction.
