  Preparing many body entangled states efficiently using available interactions
is a challenging task. One solution may be to couple a system collectively with
a probe that leaves residual entanglement in the system. We investigate the
entanglement produced between two possibly distant qubits 1 and 2 that interact
locally with a third qubit 3 under unitary evolution generated by pairwise
Hamiltonians. For the case where the Hamiltonians commute, relevant to certain
quantum nondemolition measurements, the entanglement between qubits 1 and 2 is
calculated explicitly for several classes of initial states and compared with
the case of noncommuting interaction Hamiltonians. This analysis can be helpful
to identify preferable physical system interactions for entangled state
synthesis.
