  Entanglement of high dimensional states is becoming increasingly important
for quantum communication and computing. The most common source of entangled
photons is spontaneous parametric down conversion (SPDC), where the degree of
frequency and momentum entanglement is determined by the non-linear interaction
volume. Here we show that by reducing the length of a highly non-linear
material to the micrometer scale it is possible to relax the longitudinal phase
matching condition and reach record levels of transverse wavevector
entanglement. From a micro-sized layer of lithium niobate we estimate the
number of entangled angular modes to be over 1200. The entanglement is measured
both directly using correlation measurements and indirectly using stimulated
emission tomography. The high entanglement of the state generated can be used
to massively increase the quantum information capacity of photons, but it also
opens up the possibility to improve the resolution of many quantum imaging
techniques.
