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Superselection rules (SSRs), arising from the conservation of physicalquantities such as parity or particle number, place constraints on the physicalstate space of fermionic mode systems. This affects the amount of extractablemode entanglement possessed in a given state and its manipulation by theso-called entanglement-free operations. Here, we present a set ofmajorization-based conditions for the mixed state transformations of bipartitemode entanglement, where the allowed operations (i.e., resource non-generatingoperations), that is, local operations and classical communication, arerestricted by local SSRs. We then focus on the local parity SSR and investigatethe possibility to relax the constraints imposed by it through a catalyst. Inparticular, we show that an ancillary mode system can catalyze the change inlocal parity. Finally, we discuss the application of our methodology to variousproblems in different fields. Accordingly, we propose that it may shed newlight on the activation of orbital entanglement in chemical molecules and themanipulation of multipartite entanglement or quantum discord in distinguishablequantum systems.

Manipulating fermionic mode entanglement in the presence of superselection rules