Classical randomness in quantum measurements

@article{DAriano2005ClassicalRI,
  title={Classical randomness in quantum measurements},
  author={Giacomo Mauro D’Ariano and Paoloplacido Lo Presti and Paolo Perinotti},
  journal={Journal of Physics A},
  year={2005},
  volume={38},
  pages={5979-5991}
}
Similarly to quantum states, also quantum measurements can be ‘mixed’, corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely classical nature. It is then natural to ask which apparatuses are indecomposable, i.e. do not correspond to any random choice of apparatuses. This problem is interesting not only for foundations, but also for applications, since most optimization strategies… 
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