An area law for entanglement from exponential decay of correlations

By Fernando G. S. L. Brandão, Michal Horodecki. Nature Physics, 2013

142 citations recorded by the source corpus.

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 states—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. If correlations decay exponentially in a one-dimensional quantum many-body system, then entanglement satisfies an area law. The intuitive explanation for this turns out to be wrong, but the statement is nevertheless true, as demonstrated by a proof based on quantum information theory.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/bd3952fe34ef41d10e8cbbd8b94b8f9371da11bf

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Citations in the corpus

Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “• if the state to be approximated has exponential decay of correlation functions with respect to every pair of observables (with potentially unbounded support) then an efficient polynomial approximation exists in terms of an MPS (Brandao and Horodecki, 2013).”
Adiabatic Quantum Computing (2016, background): “…a polynomial time algorithm for the ground state of 1D gapped local Hamiltonians with constant ground-state energy (Huang, 2014; Landau et al., 2015), and the fact that 1D quantum many-body states satisfying exponential decay of correlations always fulfill an area law (Brandao and Horodecki, 2013).”
Efficient tomography of a quantum many-body system (2016, background): “In 1D systems, such states can be described by a compact MPS [15, 20] and, to identify and certify the total N-component MPS, the experimentalist need only perform the measurements required to reconstruct the local reductions [16].”