  High-dimensional entanglement offers a variety of advantages for both
fundamental and applied applications in quantum information science. A central
building block for such applications is a programmable processor of entangled
states, which is crucial for the certification, manipulation and distribution
of high-dimensional entanglement. The leading technology for processing photons
is integrated multiport interferometers. However, such devices are incompatible
with structured light, and their scaling is challenging. Here, we unlock these
limitations by demonstrating a reconfigurable processor of entangled photons in
high-dimensions that is based on multi-plane light conversion (MPLC), a
technology that was recently developed for multiplexing hundreds of spatial
modes for classical communication. We use our programmable MPLC platform to
certify three-dimensional entanglement in two mutually unbiased bases, perform
400 arbitrary random transformations on entangled photons, and convert the mode
basis of entangled photons for entanglement distribution.
