  For two symmetric strips with equal and finite size and in the background of
several confining geometries, we numerically calculate the critical distance
between these two mixed systems where the mutual information between them drops
to zero and show that this quantity could be a useful correlation measure in
probing the phase structures of holographic QCD models. The models that we
consider here are Sakai-Sugimoto and deformed Sakai-Sugimoto, Klebanov-Tseytlin
and Maldacena Nunez. For evaluating the structures of these holographic
supergravity geometries from the perspective of the bulk reconstruction, we
also calculate their Crofton forms and show that there is a universal behavior
in the confining backgrounds where a "well functionality" is present around the
IR cutoff point, and far from the IR wall the scalar part of the Crofton form
would become constant, demonstrating the effects of the wall of the confining
models on the phase structures. This work is the shorter version of our
previous work arXiv:2110.12970 with few more results about the connections
between phases.
