  Distributing long-distance entanglement is a fundamental goal that is
necessary for a variety of tasks such as quantum communication, distributed
quantum computing, and quantum metrology. Currently quantum repeater schemes
typically aim to distribute one ebit at a time, the equivalent of one Bell
pair's worth of entanglement. Here we present a method to distribute a
macroscopic amount of entanglement across long-distances using a number of
operations that scales only linearly with the chain length. The scheme involves
ensembles of qubits and entangling them with an $S^z S^z$ interaction, which
can be realized using atomic gas ensembles coupled by a shared optical mode.
Using only local measurements on the intermediate ensembles, this leaves the
ensembles at the ends of the chain entangled. We show that there are particular
``magic'' interaction times that allow for distribution of entanglement with
perfect fidelity, with no degradation with chain length. The scheme is
deterministic, such that with suitable local conditional unitary corrections,
the same entangled state can always be prepared with good approximation.
