Properties and Application of Intermediate Entangled State Representation

庞乾骏

Qin Guo, Liying Jiang, Cunjin Liu +2 more

By combining the beam splitter and the Fresnel transform, a protocol is proposed to generate a new entangled state representation, called the intermediate coherent-entangled state (ICES) representation. The properties, such as eigenvalue equation, completeness relation and orthogonal relation, are investigated. The conjugate state representation of the ICES and the Schmidt decomposing of the ICES are also discussed. As applications, a new squeezing operator and some operator identities by using the ICES are obtained.

Li, Heng-Mei, Yuan +1 more

Pang Qian-Jun

We introduce the intermediate entangled state |α⟩ and discuss its properties of |α⟩ λ,ν . We obtain the expression of the two-mode Wigner operator in the |α⟩ λ,ν representation. We find that the projection operator |α⟩ λ,ν λ,ν ⟨α| is just the Radon transformation of the two-mode Wigner operator. Using the |α⟩ λ,ν representation, we successfully obtain the eigenvalues and eigenvectors of a bipartite system coupled in a quite complicated way.

Pang Qian-Jun

We introduce a generalized intermediate entangled state representation |β⟩ Λ to study the energy spectrum of an electron in a uniform magnetic field and a harmonic potential through algebraic calculation. We find that the degeneracy of the energy levels is disappeared due to the existence of the additional potential. We make it clear that the eigenfunction is just the expression of eigenvector, defined in n Fock space, in |β⟩ Λ representation.

Hong-Yi Fan, Junhua Chen, Song Tong-Qiang