  Superselection rules (SSRs), linked to the conservation of physical
quantities such as parity or particle number, impose constraints on allowable
physical operations in fermionic systems. This affects the amount of
extractable mode entanglement possessed in a given state and its manipulation
by the so-called entanglement-free operations. Here, we present a
majorization-based algorithm for the mixed state transformations of bipartite
mode entanglement, where the allowed operations (i.e., resource non-generating
operations), that is, local operations and classical communication, are
restricted by local SSRs. We then focus on the local parity SSR and investigate
the possibility to relax the constraints imposed by it through a catalyst. In
particular, we show that an ancillary mode system can catalyze the change in
local parity. Finally, we discuss the application of our methodology to various
problems in different fields. Accordingly, we propose that it may shed new
light on the activation of orbital entanglement in chemical molecules and the
manipulation of multipartite entanglement or quantum discord in distinguishable
quantum systems.
