  Light shaping facilitates the preparation and detection of optical states and
underlies many applications in communications, computing, and imaging. In this
Letter, we generalize light shaping to the quantum domain. We show that
patterns of phase modulation for classical laser light can also shape higher
orders of spatial coherence, allowing deterministic tailoring of
high-dimensional quantum entanglement. By modulating spatially entangled photon
pairs, we create periodic, topological, and random patterns of quantum
illumination, without effect on intensity. We then structure the quantum
illumination to simultaneously compensate for entanglement that has been
randomized by a scattering medium and to characterize the medium's properties
via a quantum measurement of the optical memory effect. The results demonstrate
fundamental aspects of spatial coherence and open the field of adaptive quantum
optics.
