Study For Normally Ordered Bi-variation Normal Distribution Associated With Two-mode Squeezed State Involved Entanglement And Coherence

In recent ten years, IWOP technology makes Dirac,s symbolic method be more complete,and it can express better the physica l laws, so its applica tion is gradually widespread such asinventing new representation, deriving operator Identities, studying coherent and squeezedstate,completeness rela tion and rotation of quantum so on. And it developes transformationtheory of quantum mecha nics. Although few of the articles involve in the theory , the theoryhas infiltrated into ma ny areas and has important applica tion on the group representation,molecular vibration, solid and quantum theory.In the paper [20], on the basis of the IWOP technology and the Weyl orderinginvariance under transformations, it has show that two-mode density operator withentanglement involved can be put into norma lly ordered form in the bi-variate norma ldistribution and the author analyses its margina l distribution.In this paper , we give a complex two-mode squeezed operator, and derive its densitymatrix and further extend the paper [20].We construct a two-mode squeezed state involved entanglement and coherence asfollows:After deriving its density matrix, we analys e its entanglement, study its ordered bi-variatenormal-distribution forms, it is clear that density operator of quantum statistics can beanalogous to that of mathema tical statistics , We can use mathema tical methods to deal with it,and analys e its margina l distribution, simultaneously, the varia nces can be calculated , thus thedensity matrix of quantum statistics theory has close relation with that of mathema ticalstatistics, the conclusion which we obtained from the above can be compared with that of thepaper [20], and shows wider applica tion in this paper tha n that of the paper [20].