On a Differential Geometric Viewpoint of Jaynes' Maxent Method and its   Quantum Extension
  We present a differential geometric viewpoint of the quantum MaxEnt estimate of a density operator when only incomplete knowledge encoded in the expectation values of a set of quantum observables is available. Finally, the additional possibility of considering some prior bias towards a certain density operator (the prior) is taken into account and the unsolved issues with its quantum relative entropic inference criterion are pointed out. 
S. A. Ali, Carlo Cafaro, Adom Giffin, Cosmo Lupo, Stefano Mancini
math-ph math.MP quant-ph