  The Loschmidt echo and the purity are two quantities that can provide
invaluable information about the evolution of a quantum system. While the
Loschmidt echo characterizes instability and sensitivity to perturbations,
purity measures the loss of coherence produced by an environment coupled to the
system. For classically chaotic systems both quantities display a number of --
supposedly universal -- regimes that can lead on to think of them as equivalent
quantities. We study the decay of the Loschmidt echo and the purity for systems
with finite dimensional Hilbert space and present numerical evidence of some
fundamental differences between them.
