Generating indistinguishability within identical particle systems: spatial deformations as quantum resource activators

Identical quantum subsystems can possess a property which does not have any classical counterpart: indistinguishability. As a long-debated phenomenon, identical particles' indistinguishability has been shown to be at the heart of various fundamental physical results. When concerned with the spatial degree of freedom, identical constituents can be made indistinguishable by overlapping their spatial wave functions via appropriately defined spatial deformations. By the laws of quantum mechanics, any measurement designed to resolve a quantity which depends on the spatial degree of freedom only and performed on the regions of overlap is not able to assign the measured outcome to one specific particle within the system. The result is an entangled state where the measured property is shared between the identical constituents. In this work, we present a coherent formalization of the concept of deformation in a general $N$-particle scenario, together with a suitable measure of the degree of indistinguishability. We highlight the basic differences with nonidentical particles scenarios and discuss the inherent role of spatial deformations as entanglement activators within the "spatially localized operations and classical communication" operational framework.