The q-analogues of two-mode squeezed states constructed by virtue of the IWOP technique

The $q$-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product (IWOP) of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state $S_2' (r)\left| {00} \right\rangle $ are investigated. It is found that, in different ranges of the squeezed parameter $r$, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.