Russian Journal of Mathematical Physics

, Volume 19, Issue 4, pp 417–427 | Cite as

Linear and nonlinear liftings of states of quantum systems

  • G. G. Amosov
  • V. Zh. Sakbaev
  • O. G. Smolyanov


In this paper, we study the representability of an arbitrary quantum state ρ ∈ Σ(H) as the reduction of a vector state r ∈ Σ(H) of the extended system. We extend the operation of lifting from the set of states Σ n (H) to the set of generalized states Σ(H). A method of constructing the Hilbert space H and the affine linear lifting Σ(H) → Σ(H) is studied. The construction of individual expansion H ρ of the space H for which the state ρ is a reduction of a vector state H ρ is of special interest.


Hilbert Space Tensor Product Vector State Quantum System Banach Algebra 


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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • G. G. Amosov
    • 1
  • V. Zh. Sakbaev
    • 1
  • O. G. Smolyanov
    • 2
  1. 1.Department of MathematicsMoscow Institute of Physical Engineering (Physical-Technical)Dolgoprudnyi (Moscow Region)Russia
  2. 2.Department of MathematicsLomonosov Moscow State UniversityMoscowRussia

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