The Quantum Relative Entropy as a Rate Function and Information Criteria
  We prove that the quantum relative entropy is a rate function in large deviation principle. Next, we define information criteria for quantum states and estimate the accuracy of the use of them. Most of the results in this paper are essentially based on Hiai-Ohya-Tsukada theorem. 
Kazuya Okamura
quant-ph math-ph math.MP math.PR math.ST stat.TH