Area Laws in Quantum Systems : Mutual Information and Correlations

Author(s): M. M. Wolf, F. Verstraete, M. B. Hastings, J. I. Cirac

Journal: Physical Review Letters

Volume: 100

Page(s): 070502

Year: 2008

DOI Number: 10.1103/PhysRevLett.100.070502

Link: Link to publication


The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. In this Letter we show that this phenomenon not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of degrees of freedom, it may diverge as the inverse temperature in quantum systems. It is shown that an area law is generally implied by a finite correlation length when measured in terms of the mutual information.


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