  We investigate different entanglement properties of a holographic QCD (hQCD)
model with a critical end point at finite baryon density. Firstly we consider
the holographic entanglement entropy (HEE) of this hQCD model in a spherical
shaped region and a strip shaped region, respectively, and find that the HEE of
this hQCD model in both regions can reflect QCD phase transition. What is more
is that although the area formulas and minimal area equations of the two
regions are quite different, the HEE have very similar behavior on the QCD
phase diagram. So we argue that the behavior of HEE on the QCD phase diagram is
independent of the shape of subregions. However, as we know that HEE is not a
good quantity to characterize the entanglement between different subregions of
a thermal system. So we then study the mutual information (MI), conditional
mutual information (CMI) and the entanglement of purification (Ep) in different
strip shaped regions. We find that the three entanglement quantities have very
similar behavior: their values do not change so much in the hadronic matter
phase and then rise up quickly with the increase of $T$ and $\m$ in the QGP
phase. Near the phase boundary, these three entanglement quantities change
smoothly in the crossover region, continuously but not smoothly at CEP and show
discontinuity behavior in the first phase transition region. And all of them
can be used to distinguish different phases of strongly coupled matter.
