  We consider an extended Bose-Hubbard model that includes pair-correlated
tunneling. We demonstrate that a minimal four-mode implementation of this model
exhibits a pair-correlated regime in addition to Mott insulator and superfluid
regimes. We propose a low complexity variational subspace for the ground state
of the system in the pair-correlated regime, which we find to be numerically
exact in pure pair-tunneling limit. Additionally, we propose a parameter-free
high fidelity model wave function that qualitatively captures the features of
the ground state in the pair-correlated regime. Although the operationally
accessible entanglement vanishes deep inside the Mott insulator and superfluid
regimes due to particle number conservation, we find that in the pure
pair-correlated tunneling limit the accessible entanglement entropy grows
logarithmically with the number of particles. Furthermore, we demonstrate that
upon application of a unitary beamsplitter operation, the pair-correlated
ground state is transformed into a state with completely accessible
entanglement that is not limited by super-selection rules.
