  We study relevant features of the spectrum of the quantum open baker map. The
opening consists of a cut along the momentum $p$ direction of the 2-torus phase
space, modelling an open chaotic cavity. We study briefly the classical forward
trapped set and analyze the corresponding quantum nonunitary evolution
operator. The distribution of eigenvalues depends strongly on the location of
the escape region with respect to the central discontinuity of this map. This
introduces new ingredients to the association among the classical escape and
quantum decay rates. Finally, we could verify that the validity of the fractal
Weyl law holds in all cases.
