On the coherent state representation of linear operators

P. Gluck

Ingrid C. Daubechies

Using a family of coherent state representations we obtain in a natural and coordinate-independent way an explicit realization of a projective unitary representation of the symplectic group. Dequantization of these operators gives us the corresponding classical functions.

Élliott H. Lieb, Jan Philip Solovej

Mingxia Zhan, Fang Jia, Jiali Huang +2 more

Abstract A beam splitter operator is a very important linear device in the field of quantum optics and quantum information. It can not only be used to prepare complete representations of quantum mechanics, entangled state representation, but it can also be used to simulate the dissipative environment of quantum systems. In this paper, by combining the transform relation of the beam splitter operator and the technique of integration within the product of the operator, we present the coherent state representation of the operator and the corresponding normal ordering form. Based on this, we consider the applications of the coherent state representation of the beam splitter operator, such as deriving some operator identities and entangled state representation preparation with continuous-discrete variables. Furthermore, we extend our investigation to two single and two-mode cascaded beam splitter operators, giving the corresponding coherent state representation and its normal ordering form. In addition, the application of a beam splitter to prepare entangled states in quantum teleportation is further investigated, and the fidelity is discussed. The above results provide good theoretical value in the fields of quantum optics and quantum information.

Fei Yao, Ji‐Suo Wang, Tian-Niu Xu

Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.

Élliott H. Lieb, Jan Philip Solovej