  Entanglement is one of the strongest quantum correlation, and is a key
ingredient in fundamental aspects of quantum mechanics and a resource for
quantum technologies. While entanglement theory is well settled for
distinguishable particles, there are five inequivalent approaches to
entanglement of indistinguishable particles. We analyse the different
definitions of indistinguishable particle entanglement in the light of the
locality notion. This notion is specified by two steps: i) the identification
of subsystems by means of their local operators; ii) the requirement that
entanglement represent correlations between the above subsets of operators. We
prove that three of the aforementioned five entanglement definitions are
incompatible with any locality notion defined as above.
