Unitary equivalence between ordinary intelligent states and generalized intelligent states

Details Unitary equivalence between ordinary intelligent states and generalized intelligent states Unitary equivalence between ordinary intelligent states and generalized intelligent states

2007-09-20

arxiv.org/abs/0709.3307v2

PRA 76, 053834 (2007)

Physics

Quantum Physics

published version, 4 pages

Scientific paper

10.1103/PhysRevA.76.053834

Ordinary intelligent states (OIS) hold equality in the Heisenberg uncertainty relation involving two noncommuting observables {A, B}, whereas generalized intelligent states (GIS) do so in the more generalized uncertainty relation, the Schrodinger-Robertson inequality. In general, OISs form a subset of GISs. However, if there exists a unitary evolution U that transforms the operators {A, B} to a new pair of operators in a rotation form, it is shown that an arbitrary GIS can be generated by applying the rotation operator U to a certain OIS. In this sense, the set of OISs is unitarily equivalent to the set of GISs. It is the case, for example, with the su(2) and the su(1,1) algebra that have been extensively studied particularly in quantum optics. When these algebras are represented by two bosonic operators (nondegenerate case), or by a single bosonic operator (degenerate case), the rotation, or pseudo-rotation, operator U corresponds to phase shift, beam splitting, or parametric amplification, depending on two observables {A, B}.

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