[en] Quantum-enhanced measurements use quantum mechanical effects 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), that is, an uncertainty of order 1/ N, where N is the number of quantum resources (for example, 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 that 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.