Decoherence and linear entropy increase in the quantum baker's map

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.