### Abstract

Ordinary intelligent states (OISs) hold equality in the Heisenberg uncertainty relation involving two noncommuting observables {A,B}, whereas generalized intelligent states (GISs) do so in the more generalized uncertainty relation, the Schrödinger-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) algebras which 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 pseudorotation, operator U corresponds to phase shift, beam splitting, or parametric amplification, depending on two observables {A,B}.

Original language | English |
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Article number | 053834 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 76 |

Issue number | 5 |

DOIs | |

Publication status | Published - 29 Nov 2007 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)

### Cite this

**Unitary equivalence between ordinary intelligent states and generalized intelligent states.** / Nha, Hyunchul.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Unitary equivalence between ordinary intelligent states and generalized intelligent states

AU - Nha, Hyunchul

PY - 2007/11/29

Y1 - 2007/11/29

N2 - Ordinary intelligent states (OISs) hold equality in the Heisenberg uncertainty relation involving two noncommuting observables {A,B}, whereas generalized intelligent states (GISs) do so in the more generalized uncertainty relation, the Schrödinger-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) algebras which 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 pseudorotation, operator U corresponds to phase shift, beam splitting, or parametric amplification, depending on two observables {A,B}.

AB - Ordinary intelligent states (OISs) hold equality in the Heisenberg uncertainty relation involving two noncommuting observables {A,B}, whereas generalized intelligent states (GISs) do so in the more generalized uncertainty relation, the Schrödinger-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) algebras which 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 pseudorotation, operator U corresponds to phase shift, beam splitting, or parametric amplification, depending on two observables {A,B}.

UR - http://www.scopus.com/inward/record.url?scp=36649019783&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36649019783&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.76.053834

DO - 10.1103/PhysRevA.76.053834

M3 - Article

VL - 76

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 5

M1 - 053834

ER -