  Entanglement of mixed quantum states can be quantified using the partial
transpose and its corresponding entanglement measure, the logarithmic
negativity. Recently, the notion of partial transpose has been extended to
systems of anyons, which are exotic quasiparticles whose exchange statistics go
beyond the bosonic and fermionic case. Studying the fundamental properties of
this anyonic partial transpose, we first reveal that when applied to the
special case of fermionic systems, it can be reduced to the fermionic partial
transpose or its twisted variant depending on whether or not a boundary
Majorana fermion is present. Focusing on ground state properties, we find that
the anyonic partial transpose captures both the correct entanglement scaling
for gapless systems, as predicted by conformal field theory, and the phase
transition between a topologically trivial and a nontrivial phase. For
non-abelian anyons and the bipartition geometry, we find a rich multiplet
structure in the eigenvalues of the partial transpose, the so-called negativity
spectrum, and reveal the possibility of defining both a charge- and an
imbalance-resolved negativity.
