Long-range entanglement in quantum dots with Fermi-Hubbard physics

Abstract

The range of entanglement in quantum dots, under the effect of the Coulomb interaction and the system's size, is investigated. As ququart systems, naturally described by the Fermi-Hubbard model, we show that quantum dots supply long-range entanglement up to the third neighbor. In conjunction with that and using the lower bound of concurrence, we show that the Coulomb interaction can be adjusted to create and increase entanglement between distant parties as well. A rigorous description of the pairs is given in terms of a local half-filled state associated with each pair with an electron number $N=2$ and a spin $S=0$. A thorough study of this state provides a proper explanation related to the pairwise entanglement, namely, its amount and its behavior under the effect of the Coulomb interaction together with the system's size. In addition, we show that the confinement state of quantum dots is genuinely four-partite entangled with a maximum amount for the smallest size $L=4$.