Area laws for entanglement in quantum many-body systems give useful
information about their low-temperature behaviour and are tightly connected to
the possibility of good numerical simulations. An intuition from quantum
many-body physics suggests that an area law should hold whenever there is
exponential decay of correlations in the system, a property found, for
instance, in non-critical phases of matter. However, the existence of quantum
data-hiding state--that is, states having very small correlations, yet a volume
scaling of entanglement--was believed to be a serious obstruction to such an
implication. Here we prove that notwithstanding the phenomenon of data hiding,
one-dimensional quantum many-body states satisfying exponential decay of
correlations always fulfil an area law. To obtain this result we combine
several recent advances in quantum information theory, thus showing the
usefulness of the field for addressing problems in other areas of physics.Comment: 8 pages, 3 figures. Short version of arXiv:1206.2947 Nature Physics
(2013
