  We study two entanglement measures in a large family of systems including
incompressible quantum Hall states: the logarithmic negativity (LN), and mutual
information (MI). For pure states, obtained for example from a bipartition at
zero temperature, these provide distinct characterizations of the entanglement
present between two spatial subregions, while for mixed states (such as at
finite temperature) only the LN remains a good entanglement measure. Our focus
is on regions that have corners, either adjacent or tip-touching. We first
obtain non-perturbative properties regarding the geometrical dependence of the
LN and MI in a large family of isotropic states, including fractional quantum
Hall states. A close similarity is observed with mutual charge fluctuations,
where super-universal angle dependence holds. For the MI, we make stronger
statements due to strong subadditivity. We also give ramifications of our
general analysis to conformal field theories (CFTs) in two spatial dimensions.
We then explicitly verify these properties with integer quantum Hall states. To
do so we develop two independent approaches to obtain the fermionic LN, which
takes into account Fermi statistics: an overlap-matrix method, and a real-space
lattice discretization. At finite temperature, we find a rapid decrease of the
LN well inside the cyclotron gap at integer fillings. We further show that the
LN decays faster compared to the MI at high temperatures.
