  Quantum-enhanced measurements use quantum mechanical effects in order to
enhance the sensitivity of the measurement of classical quantities, such as the
length of an optical cavity. The major goal is to beat the standard quantum
limit (SQL), i.e. a uncertainty of order 1/\sqrt{N}, where N is the number of
quantum resources (e.g. the number of photons or atoms used), and to achieve a
scaling 1/N, known as the Heisenberg limit. So far very few experiments have
demonstrated an improvement over the SQL. The required quantum states are
generally highly entangled, difficult to produce, and very prone to
decoherence. Here we show that Heisenberg limited measurements can be achieved
without the use of entangled states by coupling the quantum resources to a
common environment which can be measured at least in part. The method is robust
under decoherence, and in fact the parameter dependence of collective
decoherence itself can be used to reach a 1/N scaling.
