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Area Laws in Quantum Systems: Mutual Information and Correlations
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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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“Thus we see that, as one might expect from our discussion around (3.19), the presence of nonzero correlation between O and X E puts a limit on how accurately we can correct for the erasure of E .”
From Bulk locality and quantum error correction in AdS/CFT (2015) · cites this paper as [31]
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Metadata
- Authors
- Wolf, M. M., Verstraete, F., Hastings, M. B., & Cirac, J. I.
- Affiliations
- Max Planck Society (DE)
- University of Vienna (AT)
- Los Alamos National Laboratory (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2008-02-20
- Volume
- 100
- Issue
- 7
- Pages
- 070502-070502
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2014461107
- Cited by
- 696
- References
- 37
- Citations by year
- 2026: 28 · 2025: 58 · 2024: 43 · 2023: 58 · 2022: 68 · 2021: 35 · 2020: 43 · 2019: 50 · 2018: 41 · 2017: 21 · 2016: 39 · 2015: 48 · 2014: 43 · 2013: 42 · 2012: 18
- FWCI
- 11.42
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (DE-AC52-06NA2-5396, AC52-06NA25396)
- Deutsche Forschungsgemeinschaft
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- area law, holographic principle, mutual information, quantum correlations, finite correlation length, lattice model, thermal equilibrium
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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