  A parameter whose coupling to a quantum probe of $n$ constituents includes
all two-body interactions between the constituents can be measured with an
uncertainty that scales as $1/n^{3/2}$, even when the constituents are
initially unentangled. We devise a protocol that achieves the $1/n^{3/2}$
scaling without generating any entanglement among the constituents, and we
suggest that the protocol might be implemented in a two-component Bose-Einstein
condensate.
