We investigate the single-particle multi-mode "entanglement" and raise the questions: Is a single particle always entangled? Is entanglement a physical reality which is invariant under an arbitrary unitary transformation or choice of mode basis? We show that, if accepting the single-particle entanglement picture, a single particle can always be entangled by choosing a proper mode basis. This "mode entanglement", expressed as a superposition of single-particle mode basis, may have important applications in quantum information processing as it has some similar mathematical features as the multi-particle entanglement.
We investigate the single-particle multi-mode "entanglement" and raise the questions: Is a single particle always entangled? Is entanglement a physical reality which is invariant under an arbitrary unitary transformation or choice of mode basis? We show that, if accepting the single-particle entanglement picture, a single particle can always be entangled by choosing a proper mode basis. This "mode entanglement", expressed as a superposition of single-particle mode basis, may have important applications in quantum information processing as it has some similar mathematical features as the multi-particle entanglement.
Single-particle entanglement entropy (SPEE) is calculated for entanglement Hamiltonian eigenmode in a one-dimensional free fermion model that undergoes a delocalized–localized phase transition. In this numerical study, we show that SPEE of entanglement Hamiltonian eigenmode has the same behavior as SPEE of Hamiltonian eigenmode at the Fermi level: as we go from delocalized phase toward localized phase, SPEE of both modes decrease in the same manner. Furthermore, fluctuations of SPEE of entanglement Hamiltonian eigenmode — which can be obtained through the calculation of moments of SPEE — signature very sharply the phase transition point. These two modes are also compared by calculation of single-particle Rényi entropy (SPRE). We show that SPEE and SPRE of entanglement Hamiltonian eigenmode can be used as phase detection parameters.