By considering two single-mode Gaussian states at the input of a beam splitter, it is seen that the entanglement of the output two-mode Gaussian state depends on the difference between the degrees of nonclassicality of the input states [1,2]. It is noticed that the greater (smaller) the difference between the two non-classicalities, the greater (smaller) is the entanglement of the output two-mode Gaussian state. Intuitively one would expect that the more nonclassical any of the input state, the more is the entanglement of the output state, but apparently, this is not the case [1,2]. Why? Can anyone explain this?

Thanks

[1] Chinese Phys. 15, 2947 (2006).

[2] J. Phys. B: At. Mol. Opt. Phys. 53, 135501 (2020).