Exponential Decay of Correlations Implies Area Law

@article{Brando2015ExponentialDO,
  title={Exponential Decay of Correlations Implies Area Law},
  author={Fernando G. S. L. Brand{\~a}o and Michal Horodecki},
  journal={Communications in Mathematical Physics},
  year={2015},
  volume={333},
  pages={761-798}
}
We prove that a finite correlation length, i.e., exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the state, thus reproducing as a particular case Hastings’s proof of an area law for groundstates of 1D gapped Hamiltonians. As a consequence, we show that 1D quantum states with exponential decay of correlations have an efficient classical approximate description as… 
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