Unitary equivalence between ordinary intelligent states and generalized intelligent states

摘要

Ordinary intelligent states (OIS) hold equality in the Heisenberg uncertaintyrelation involving two noncommuting observables {A, B}, whereas generalizedintelligent 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 anarbitrary GIS can be generated by applying the rotation operator U to a certainOIS. 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 havebeen extensively studied particularly in quantum optics. When these algebrasare represented by two bosonic operators (nondegenerate case), or by a singlebosonic operator (degenerate case), the rotation, or pseudo-rotation, operatorU corresponds to phase shift, beam splitting, or parametric amplification,depending on two observables {A, B}.