  The study of nonclassical properties of two-mode quantum states is
particularly useful in quantum information theory because of the possibilities
of obtaining entanglement and other two-mode quantum correlations in these
states. Here we have investigated the possibilities of the existence of
nonclassicality in a two-mode New generalized binomial state (TMNGBS).
Specifically two-mode antibunching, Quadrature squeezing, sum \& difference
squeezing, and various entanglement criteria e.g Shchukin-Vogel entanglement
criterion, the uncertainty relation of SU(1,1) Algebra and EPR entanglement
criterion are explored in two mode particular example of quantum state named as
New generalized binomial state. Earlier we studied nonclassicality in
single-mode NGBS, here we are extending our study toward the two-mode version
of a quantum state. Here we provide the general expressions of moments for a
two-mode quantum state (Fock basis) and explore the quantification in a
particular example NGBS. It is found that antibunching, squeezing, and SV
entanglement are possible with different limits of depending parameters but the
entanglement criteria (EPR, SU (1,1) algebra and Cauchy - Schwarz inequality
based)for NGBS are not possible. This study opens up the possibility of
exploring the two-mode nonclassicality in other states too.
