  Any given density matrix can be represented as an infinite number of
ensembles of pure states. This leads to the natural question of how to uniquely
select one out of the many, apparently equally suitable, possibilities.
Following Jaynes' information-theoretic perspective, this can be framed as an
inference problem. We propose the Maximum Geometric Quantum Entropy Principle
to exploit the notions of Quantum Information Dimension and Geometric Quantum
Entropy. These allow us to quantify the entropy of fully arbitrary ensembles
and select the one that maximizes it. After formulating the principle
mathematically, we give the analytical solution to the maximization problem in
a number of cases and discuss the physical mechanism behind the emergence of
such maximum entropy ensembles.
