  We study various holographic pure and mixed state entanglement measures in
the confined/deconfined phases of a bottom-up AdS/QCD model in the presence of
a background magnetic field. We analyse the entanglement entropy, entanglement
wedge cross-section, mutual information, and entanglement negativity and
investigate how a background magnetic field leaves its imprints on the
entanglement structure of these measures. Due to the anisotropy introduced by
the magnetic field, we find that the behaviour of these measures depends
nontrivially on the relative orientation of the strip with respect to the
field. In the confining phase, the entanglement entropy and negativity undergo
a phase transition at the same critical strip length, the magnitude of which
increases/decreases for parallel/perpendicular orientation of the magnetic
field. The entanglement wedge cross-section similarly displays discontinuous
behaviour each time a phase transition between different entangling surfaces
occurs, while further exhibiting anisotropic features with a magnetic field. We
further find that the magnetic field also introduces substantial changes in the
entanglement measures of the deconfined phase, however, these changes remain
qualitatively similar for all orientations of the magnetic field. We further
study the inequality involving entanglement wedge and mutual information and
find that the former always exceeds half of the latter everywhere in the
parameter space of the confined/deconfined phases.
