  Decoherence induced by coupling a system with an environment may display
universal features. Here we demostrate that when the coupling to the system
drives a quantum phase transition in the environment, the temporal decay of
quantum coherences in the system is Gaussian with a width independent of the
system-environment coupling strength. The existence of this effect opens the
way for a new type of quantum simulation algorithm, where a single qubit is
used to detect a quantum phase transition. We discuss possible implementations
of such algorithm and we relate our results to available data on universal
decoherence in NMR echo experiments.
