  We compare and contrast the entangling properties of a three-well
Bose-Hubbard model and an optical beamsplitter. The coupling between the
different modes is linear in both cases, and we may identify two output modes.
Obvious differences are that our Bose-Hubbard model, with only the middle well
initially occupied, does not have a vacuum input port, there is no equivalent
of a collisional, $\chi^{(3)}$ nonlinearity with the beamsplitter, and the
results of the Bose-Hubbard model show a time-dependence. In the
non-interacting case, we obtain analytic solutions and show that, like a
beamsplitter, the Bose-Hubbard system will not produce entanglement for
classical initial states. We also show that whether inseparability or
entanglement are detected depends sensitively on the criteria measured, with
different criteria giving contradictory predictions.
