Manipulating fermionic mode entanglement in the presence of superselection rules

Abstract

Superselection rules (SSRs), arising from the conservation of physical quantities such as parity or particle number, place constraints on the physical state space of fermionic mode 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 set of majorization-based conditions 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.