On classical and quantum liftings
  We analyze the procedure of lifting in classical stochastic and quantum systems. It enables one to `lift' a state of a system into a state of `system+reservoir'. This procedure is important both in quantum information theory and the theory of open systems. We illustrate the general theory of liftings by a particular class related to so called circulant states. 
L. Accardi, D. Chru\'sci\'nski, A. Kossakowski, T. Matsuoka, M. Ohya
quant-ph math-ph math.MP