Quantum local asymptotic normality based on a new quantum likelihood   ratio
  We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter. 
Koichi Yamagata, Akio Fujiwara, Richard D. Gill
quant-ph math.ST stat.AP stat.TH