  We study the quantum-classical correspondence of an experimentally accessible
system of interacting bosons in a tilted triple-well potential. With the
semiclassical analysis, we get a better understanding of the different phases
of the quantum system and how they could be used for quantum information
science. In the integrable limits, our analysis of the stationary points of the
semiclassical Hamiltonian reveals critical points associated with second-order
quantum phase transitions. In the nonintegrable domain, the system exhibits
crossovers. Depending on the parameters and quantities, the quantum-classical
correspondence holds for very few bosons. In some parameter regions, the ground
state is robust (highly sensitive) to changes in the interaction strength (tilt
amplitude), which may be of use for quantum information protocols (quantum
sensing).
