Entanglement versus gap, quantum teleportation, and the AKLT model

Quantum-mechanical entanglement is notoriously volatile because of its susceptibility to external disturbances. However, entanglement can be stabilized if it is present in the non-degenerate ground state of a gapped, time-independent Hamiltonian. In this paper, we devise a spin-chain Hamiltonian whose ground state contains a Bell pair, with one member of the pair at each end of the chain. We study the Hamiltonian numerically, using full numerical diagonalization and a carefully tailored mean-field theory, to show that it is gapped. Whenever the Hamiltonian is tuned to increase its gap, the fidelity of its Bell pair decreases, manifesting a fundamental contention. The form of the Hamiltonian is motivated by quantum teleportation. Comparing it to the canonical Affleck, Kennedy, Lieb, and Tasaki (AKLT) model, we find that the AKLT model exhibits a sort of 'failed quantum teleportation'.