  A theory of spontaneous parametric down-conversion, which gives rise to a
quantum state that is entangled in multiple parameters, such as
three-dimensional wavevector and polarization, allows us to understand the
unusual characteristics of fourth-order quantum interference in many
experiments, including ultrafast type-II parametric down-conversion, the
specific example illustrated in this paper. The comprehensive approach provided
here permits the engineering of quantum states suitable for quantum information
schemes and new quantum technologies.
