Linear and nonlinear liftings of states of quantum systems
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 Σn(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 Hρ of the space H for which the state ρ is a reduction of a vector state Hρ is of special interest.
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