  We study interacting dipolar atomic bosons in a triple-well potential within
a ring geometry. This system is shown to be equivalent to a three-site
Bose-Hubbard model. We analyze the ground state of dipolar bosons by varying
the effective on-site interaction. This analysis is performed both numerically
and analytically by using suitable coherent-state representations of the ground
state. The latter exhibits a variety of forms ranging from the su(3) coherent
state in the delocalization regime to a macroscopic cat-like state with fully
localized populations, passing for a coexistence regime where the ground state
displays a mixed character. We characterize the quantum correlations of the
ground state from the bi-partition perspective. We calculate both numerically
and analytically (within the previous coherent-state representation) the
single-site entanglement entropy which, among various interesting properties,
exhibits a maximum value in correspondence to the transition from the cat-like
to the coexistence regime. In the latter case, we show that the ground-state
mixed form corresponds, semiclassically, to an energy exhibiting two
almost-degenerate minima.
