  We study the baker's map and its Walsh quantization, as a toy model of a
quantized chaotic system. We focus on localization properties of eigenstates,
in the semiclassical regime. Simple counterexamples show that quantum unique
ergodicity fails for this model. We obtain, however, lower bounds on the
entropies associated with semiclassical measures, as well as on the Wehrl
entropies of eigenstates. The central tool of the proofs is an "entropic
uncertainty principle".
