Universal Preparability of States and Asymptotic Completeness

Rolf Gohm, Florian Haag, Burkhard Kuemmerer

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Abstract

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 B(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 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.
Original languageEnglish
Pages (from-to)59-94
Number of pages36
JournalCommunications in Mathematical Physics
Volume352
Issue number1
Early online date07 Mar 2017
DOIs
Publication statusPublished - 16 Mar 2017

Keywords

  • repeated interaction
  • transition
  • preparability
  • tightness
  • stationary Markov chain
  • asymptotic completeness
  • controllability
  • observability
  • micromaser

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