The generalized coherent states and quantum information

Applications of the generalized coherent states proposed by Klauder and modified by Gaeeau and Klauder will be investigated. Klauder's coherent states are defined on energy eigenstates rather than the number states. Thus they are applicable to a wide class of systems. First, using Klauder's coherent states, we formally constructed the coherent states for the Coulomb problem in a curved space of positive constant curvature. Then we consider the flat space limit. We show that the coherent states for the discrete spectrum of the system in curved space split into two portions corresponding to the discrete and the continuous spectrum for a fixed f wave sector of the hydrogen atom in flat space. This approach provides both the discrete coherent states and the continuous coherent states for the hydrogen atom in a unified and natural manner. For the purpose of comparison, we consider the Fukui-Aizawa coherent states which are formulated on the basic of supersymmetric quantum mechanics. We construct another set of coherent states for the hydrogen atom with the help of the Fukui-Aizawa method. We see that the two sets of coherent states we thus construct are very similar but different from each other by exponential factors. As the second area of applications of Klauder's coherent states, we consider quantum information processing. Following Fivel's definition, we construct two sets of the generalized Bell states by means of Klauder's coherent states for a two-level system and three-level systems. We calculate the concurrence of an entangled coherent states. We show that a superposition of Klauder's coherent states may be teleported via a standard Bell state channel. The desired coherent states are recovered by an additional orthogonal transformation. Finally we discuss appropriate physical quantities that the sender of the coherent states can measure for the teleportation.