  We study the entanglement wedge cross-section (EWCS) in holographic Aether
gravity theory, a gravity theory with Lorentz symmetry violation while keeping
the general covariance intact. We find that only a limited parameter space is
allowed to obtain a black brane with positive Hawking temperature. Subject to
these allowed parameter regions, we find that the EWCS could exhibit
non-monotonic behaviors with system parameters. Meanwhile, the holographic
entanglement entropy (HEE), and the corresponding mutual information (MI), can
only exhibit monotonic behaviors. These phenomena suggest that the EWCS could
capture much more rich content of the entanglement than that of the HEE and the
MI. The role of the Lorentz violation in determining the behaviors of quantum
information-related quantities is also analyzed.
