  We show that the coarse-grained quantum baker's map exhibits a linear entropy
increase at an asymptotic rate given by the Kolmogorov-Sinai entropy of the
classical chaotic baker's map. The starting point of our analysis is a symbolic
representation of the map on a string of $N$ qubits, i.e., an $N$-bit register
of a quantum computer. To coarse-grain the quantum evolution, we make use of
the decoherent histories formalism. As a byproduct, we show that the condition
of medium decoherence holds asymptotically for the coarse-grained quantum
baker's map.
