  Entangled quantum systems have properties that have fundamentally overthrown
the classical worldview. Increasing the complexity of entangled states by
expanding their dimensionality allows the implementation of novel fundamental
tests of nature, and moreover also enables genuinely new protocols for quantum
information processing. Here we present the creation of a (100x100)-dimensional
entangled quantum system, using spatial modes of photons. For its verification
we develop a novel nonlinear criterion which infers entanglement dimensionality
of a global state by using only information about its subspace correlations.
This allows very practical experimental implementation as well as highly
efficient extraction of entanglement dimensionality information. Applications
in quantum cryptography and other protocols are very promising.
