  We show the continuity property of spectral gaps and complete Logarithmic
constants in terms of the jump operators of Lindblad generators in finite
dimensional setting. Our method is based on the bimodule structure of the
derivation space and the technique developed in [Paulsen09]. Using the same
trick, we also show the continuity of the $g^2(0)$ constant used to distinguish
quantum and classical lights in quantum optics.
