This thesis casts new light on quantum entanglement of photons with
complex spatial patterns due to direct coincidence imaging. It
demonstrates novel methods to generate, investigate, and verify
entanglement of complex spatial structures. Quantum theory is one
of the most successful and astonishing physical theories. It made
possible various technical devices like lasers or mobile phones
and, at the same time, it completely changed our understanding of
the world. Interestingly, such counterintuitive features like
entanglement are an important building block for future quantum
technologies. In photonic experiments, the transverse spatial
degree of freedom offers great potential to explore fascinating
phenomena of single photons and quantum entanglement. It was
possible to verify the entanglement of two photons with very high
quanta of orbital angular momentum, a property of photons connected
to their spatial structure and theoretically unbounded. In
addition, modern imaging technology was used to visualize the
effect of entanglement even in real-time and to show a surprising
property: photons with complex spatial patterns can be both
entangled and not entangled in polarization depending on their
transverse spatial position.
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