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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The presence of nonzero correlation between O and X_E puts a limit on how accurately one can correct for the erasure of E.
“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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- 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 › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- area law, holographic principle, mutual information, quantum correlations, finite correlation length, lattice model, thermal equilibrium
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