Correlations of measurement information and noise in quantum   measurements with finite resolution
  The original purpose of measurements is to provide us with information about a previously unknown physical property of the system observed. In the Hilbert space formalism of quantum mechanics, this physical meaning of measurement information is not immediately apparent. In order to study the relationship between the Hilbert space coherence of the quantum state and the measurement information obtained in the laboratory, we introduce a generalized measurement postulate for finite resolution measurements. With this measurement model, correlations between non-commuting observables can be investigated. These experimentally accessible correlations reveal nonclassical features in their dependence on the operator ordering, reflecting the particular measurement context by which they are determined. 
Holger F. Hofmann, Takayoshi Kobayashi, and Akira Furusawa