  Exploiting the split property of quantum field theories (QFTs), a notion of
von Neumann entropy associated to pairs of spatial subregions has been recently
proposed both in the holographic context -- where it has been argued to be
related to the entanglement wedge cross section -- and for general QFTs. We
argue that the definition of this "reflected entropy" can be canonically
generalized in a way which is particularly suitable for orbifold theories --
those obtained by restricting the full algebra of operators to those which are
neutral under a global symmetry group. This turns out to be given by the
full-theory reflected entropy minus an entropy associated to the expectation
value of the "twist" operator implementing the symmetry operation. Then we show
that the reflected entropy for Gaussian fermion systems can be simply written
in terms of correlation functions and we evaluate it numerically for two
intervals in the case of a two-dimensional Dirac field as a function of the
conformal cross-ratio. Finally, we explain how the aforementioned twist
operators can be constructed and we compute the corresponding expectation value
and reflected entropy numerically in the case of the $\mathbb{Z}_2$ bosonic
subalgebra of the Dirac field.
