Single-Particle Entanglement

This review is about single-particle entanglement. Entanglement occurs when the state of a quantum system with at least two degrees of freedom has a particular non-separable form. In the case of single-particle entanglement, this quantum correlation is shared by the same particle being it a photon, a neutron, an ion, or an atom. Here, the basics of quantum entanglement are discussed focusing on the case it is related to the degrees of freedom of a single particle. It is discussed how the violation of peculiar inequalities in this context rules out any realistic non-contextual hidden variable theory alternative to quantum mechanics. Moreover, experiments that demonstrate single-particle entanglement for photons, neutrons, and atoms are discussed. Finally, the applications of single-particle entanglement as a resource for quantum information are discussed and specifically quantum key distribution is detailed, where the use of single-particle entangled photons allows to improve the security of the BB84 protocol.