Universal Preparability of States and Asymptotic Completeness


We introduce a notion of universal preparability for a state of a system, more precisely: for a normal state on a von Neumann algebra. It describes a situation where from an arbitrary initial state it is possible to prepare a target state with arbitrary precision by a repeated interaction with a sequence of copies of another system. For \({\mathcal{B}(\mathcal{H})}\) we give criteria sufficient to ensure that all normal states are universally preparable which can be verified for a class of non-commutative birth and death processes realized, in particular, by the interaction of a micromaser with a stream of atoms. As a tool, the theory of tight sequences of states and of stationary states is further developed and we show that in the presence of stationary faithful normal states universal preparability of all normal states is equivalent to asymptotic completeness, a notion studied earlier in connection with the scattering theory of non-commutative Markov processes.


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Correspondence to Rolf Gohm.

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Communicated by M. M. Wolf

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Gohm, R., Haag, F. & Kümmerer, B. Universal Preparability of States and Asymptotic Completeness. Commun. Math. Phys. 352, 59–94 (2017). https://doi.org/10.1007/s00220-017-2851-8

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