  Understanding gravity in the framework of quantum mechanics is one of the
great challenges in modern physics. Along this line, a prime question is to
find whether gravity is a quantum entity subject to the rules of quantum
mechanics. It is fair to say that there are no feasible ideas yet to test the
quantum coherent behaviour of gravity directly in a laboratory experiment.
Here, we introduce an idea for such a test based on the principle that two
objects cannot be entangled without a quantum mediator. We show that despite
the weakness of gravity, the phase evolution induced by the gravitational
interaction of two micron size test masses in adjacent matter-wave
interferometers can detectably entangle them even when they are placed far
apart enough to keep Casimir-Polder forces at bay. We provide a prescription
for witnessing this entanglement, which certifies gravity as a quantum coherent
mediator, through simple correlation measurements between two spins: one
embedded in each test mass. Fundamentally, the above entanglement is shown to
certify the presence of non-zero off-diagonal terms in the coherent state basis
of the gravitational field modes.
