  Consider the question: what statistical ensemble corresponds to minimal prior
knowledge about a quantum system ? For the case where the system is in fact
known to be in a pure state there is an obvious answer, corresponding to the
unique unitarily-invariant measure on the Hilbert sphere. However, the problem
is open for the general case where states are described by density operators.
Here two approaches to the problem are investigated.
  The first approach assumes that the system is randomly correlated with a
second system, where the ensemble of composite systems is described by a random
pure state. Results for qubits randomly correlated with other systems are
presented, including average entanglement entropies. It is shown that maximum
correlation is guaranteed in the limit as one system becomes
infinite-dimensional.
  The second approach relies on choosing a metric on the space of density
operators, and generating a corresponding ensemble from the induced volume
element. Comparisons between the approaches are made for qubits, for which the
second approach (based on the Bures metric) yields the most symmetric, and
hence the least informative, ensemble of density operators.
