We present a broad family of quantum baker maps that generalize the proposal of Schack and Caves to any even Hilbert space with arbitrary boundary conditions. We identify a structure, common to all maps consisting of a simple kernel perturbed by diffraction effects. This “essential” baker’s map has a different semiclassical limit and can be diagonalized analytically for Hilbert spaces spanned by qubits. In all cases this kernel provides an accurate approximation to the spectral properties—eigenvalues and eigenfunctions—of all the different quantizations.

• Received 7 June 2006

DOI:https://doi.org/10.1103/PhysRevE.74.046205