  All matter is made up of fermions -- one of the fundamental type of particles
in nature. Fermions follow the Pauli exclusion principle, stating that two or
more identical fermions cannot occupy the same quantum state. Antisymmetry of
the fermionic wavefunction, however, implies additional constraints on the
natural occupation numbers. These constraints depend on the dimensionality and
purity of the system and have so far not been explored experimentally. Here, we
propose an experiment in a system of multiple quantum dots capable of producing
the highly entangled fermionic states necessary to reach the regime, where
these additional constraints become dominant and can be probed. The type and
strength of the required multi-fermion entanglement provides barriers to
reaching deep into this regime. Transcending these barriers thus serves as a
testing ground for the capabilities of future fermionic quantum information
processing as well as quantum computer architectures based on fermionic states.
