  Two of us (CM and VV) recently showed how the quantum character of a physical
system, in particular the gravitational field, can in principle be witnessed
without directly measuring observables of that system, solely by its ability to
mediate entanglement between two other systems. Here we propose a variant of
that scheme, where the entanglement is again generated via gravitational
interaction, but now between two particles both at sharp locations (very close
to each other) but each in a superposition of two different masses. We discuss
an in-principle example using two hypothetical massive, neutral,
weakly-interacting particles generated in a superposition of different masses.
The key property of such particles would be that, like neutrinos, they are
affected only by weak nuclear interactions and gravity.
