  We analyze two two-mode continuous variable separable states with the same
marginal states. We adopt the definition of classicality in the form of
well-defined positive Wigner function describing the state and find that
although the states possess positive local Wigner functions, they exhibit
negative Wigner functions for the global states. Using the negativity of Wigner
function as an indicator of nonclassicality, we show that despite these states
possess different negativities of the Wigner function, they do not reveal this
difference as phase space nonclassicalities such as negativity of the Mandel
$Q$ parameter or quadrature squeezing. We then concentrate on quantum
correlation of these states and show that quantum discord and local quantum
uncertainty, as two well-defined measures of quantum correlation, manifest the
difference between negativity of the Wigner functions. The non-Gaussianity of
these states is also examined and show that the difference in behavior of their
non-Gaussianity is the same as the difference between negativity of their
Wigner functions. We also investigate the influence of correlation rank
criterion and find that when the states can be produced locally from classical
states, the Wigner functions can not reveal their quantum correlations.
