Unitary equivalence between ordinary intelligent states and generalized intelligent states

TL;DR

This paper demonstrates that ordinary and generalized intelligent states are unitarily equivalent through specific transformations, linking their properties in quantum optics contexts such as su(2) and su(1,1) algebras.

Contribution

It establishes a unitary equivalence between OIS and GIS, showing how GIS can be generated from OIS via rotation operators in algebraic quantum systems.

Findings

OIS are a subset of GIS in uncertainty relations.

Unitary transformations relate OIS and GIS in su(2) and su(1,1) algebras.

Transformations include phase shifts, beam splitting, and parametric amplification.

Abstract

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}.