  At sufficiently low temperature, without requiring any numerical data at
finite real chemical potential, we can clarify the canonical partition function
with fixed quark number via the imaginary chemical potential region with few
ansatzs. The canonical partition function relates to the multiplicity
distribution which can be observed in collider experiments and thus we may
access important information of the properties of the QCD matter based on the
canonical method. In this paper, we estimate the multiplicity entropy, the
configuration entropy, and the pointwise information which can be calculable
with the canonical partition function to understand the properties of the cold
QCD matter at finite density. With the large $N_\mathrm{c}$ limit where
$N_\mathrm{c}$ is the number of colors, we can simply estimate the tendency of
them, and then the relation to the quarkyonic phase is clarified. In addition,
we discuss the nontrivial ground state degeneracy from the viewpoint of the
canonical sectors.
