Quantum Identity and Indistinguishability

Dennis Dieks

Lars‐Göran Johansson

Matteo Piccolini, Farzam Nosrati, Gerardo Adesso +2 more

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 non-identical particles scenarios and discuss the inherent role of spatial deformations as entanglement activators within the spatially localized operations and classical communication operational framework. This article is part of the theme issue ‘Identity, individuality and indistinguishability in physics and mathematics’.

Kostya Trachenko

Matteo Piccolini, Marcin Karczewski, Jin-Shi Xu +5 more

Identical particles underpin most quantum technologies, but the role of indistinguishability in these processes extends far beyond the symmetrization of many-particle states. This Colloquium presents a unified operational perspective on how particle identity, indistinguishability, exchange statistics, and many-particle interference can instead be harnessed as resources for quantum information processing. We first clarify the notions of entanglement and indistinguishability for identical particles, emphasizing their dependence on the accessible measurements and information. We then review how spatial overlap, multiparticle interference, and path identity enable the generation, extraction, protection, and distillation of coherence and entanglement. Their applications to quantum metrology and imaging, state discrimination, teleportation, entanglement swapping, and quantum cloning are examined. Finally, we discuss the thermodynamic role of indistinguishability, from the Gibbs paradox to quantum thermal machines and statistics-driven engines. Across these settings, indistinguishability emerges as a controllable, task-dependent resource whose benefits are determined by state preparation, exchange statistics, interference, and measurement constraints.

Inna G Kaplan

The connection between the exclusion principle and the principle of indistinguishability of identical particles in quantum mechanics is discussed. It is shown with the aid of a density matrix defined for states with arbitrary permutation symmetry that the particles are indistinguishable only for one-dimensional representations of the permutation group (symmetrical and antisymmetrycal), and are distinguishable in all the states that are degenerate in the permutations. It is demonstrated by the same token that the exclusion principle follows from the principle of indistinguishability of identical particles and the Pauli theorem on the connection between spin and statistics.