# 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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