TY - JOUR

T1 - Linear and nonlinear liftings of states of quantum systems

AU - Amosov, G. G.

AU - Sakbaev, V. Zh

AU - Smolyanov, O. G.

PY - 2012/12/1

Y1 - 2012/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84871103337&partnerID=8YFLogxK

U2 - 10.1134/S1061920812040024

DO - 10.1134/S1061920812040024

M3 - Article

AN - SCOPUS:84871103337

VL - 19

SP - 417

EP - 427

JO - Russian Journal of Mathematical Physics

JF - Russian Journal of Mathematical Physics

SN - 1061-9208

IS - 4

ER -