Taming identical particles for discerning the genuine non-locality

Abstract

This work provides a comprehensive approach to analyze the entanglement between subsystems generated by identical particles, based on the symmetric/exterior algebra (SEA) and microcausality. Our method amends the no-labeling approach (NLA) to quantify any type of identical particles' entanglement, especially fermions with the parity superselection rule. We can analyze the non-local properties of identical particles' states in a fundamentally equivalent way to those for non-identical particles, which is achieved by the factorizability of the total Hilbert space of identical particles. This formal correspondence between identical and non-identical particle systems turns out to be useful for quantifying the non-locality generated by identical particles, such as the maximal CHSH inequality violation and the GHJW theorem of identical particles.