The DOI matches its Crossref record; 35 of the 37 references it cites were found in a registry or an index.
Area Laws in Quantum Systems: Mutual Information and Correlations
Open accessAbstract
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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Cites
Quantum Computation and Quantum Information
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,450
Fault-tolerant quantum computation by anyons
Kitaev, A. Y. (2003) · Annals of Physics · doi:10.1016/s0003-4916(02)00018-0 · Cited by 7,238
Raussendorf, R., & Briegel, H. J. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5188 · Cited by 4,477
Entanglement entropy and quantum field theory
Calabrese, P., & Cardy, J. (2004) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2004/06/p06002 · Cited by 3,275
Entanglement in Quantum Critical Phenomena
Vidal, G., Latorre, J. I., Rico, E., & Kitaev, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.227902 · Cited by 2,793
Persistent Entanglement in Arrays of Interacting Particles
Briegel, H. J., & Raussendorf, R. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.910 · Cited by 1,950
Scaling of entanglement close to a quantum phase transition
Osterloh, A., Amico, L., Falci, G., & Fazio, R. (2002) · Nature · doi:10.1038/416608a · Cited by 1,860
Srednicki, M. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.666 · Cited by 1,858
Entanglement in a simple quantum phase transition
Osborne, T. J., & Nielsen, M. A. (2002) · Physical Review A · doi:10.1103/physreva.66.032110 · Cited by 1,472
Quantum source of entropy for black holes
Bombelli, L., Koul, R. K., Lee, J., & Sorkin, R. D. (1986) · Physical Review D · doi:10.1103/physrevd.34.373 · Cited by 1,439
Finitely correlated states on quantum spin chains
Fannes, M., Nachtergaele, B., & Werner, R. F. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02099178 · Cited by 1,422
On the quantum structure of a black hole
't Hooft, G. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90418-3 · Cited by 1,311
Vidal, G. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.220405 · Cited by 1,206
Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems
Verstraete, F., García-Ripoll, J. J., & Cirac, J. I. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.207204 · Cited by 1,098
Self-citationCallan, C., & Wilczek, F. (1994) · Physics Letters B · doi:10.1016/0370-2693(94)91007-3 · Cited by 826
Ohya, M., & Petz, D. (1993) · doi:10.1007/978-3-642-57997-4 · Cited by 764
Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensionsPreprint
Verstraete, F., & Cirac, J. I. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.cond-mat/0407066 · Cited by 672
Self-citationQuantum, classical, and total amount of correlations in a quantum state
Groisman, B., Popescu, S., & Winter, A. (2005) · Physical Review A · doi:10.1103/physreva.72.032317 · Cited by 632
Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States
Verstraete, F., Wolf, M. M., Perez-Garcia, D., & Cirac, J. I. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.220601 · Cited by 580
Self-citationQuantum Spin Chain, Toeplitz Determinants and the Fisher—Hartwig Conjecture
Jin, B.-Q., & Korepin, V. E. (2004) · Journal of Statistical Physics · doi:10.1023/b:joss.0000037230.37166.42 · Cited by 505
Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture
Gioev, D., & Klich, I. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.100503 · Cited by 498
Entanglement versus Correlations in Spin Systems
Verstraete, F., Popp, M., & Cirac, J. I. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.027901 · Cited by 470
Self-citationViolation of the Entropic Area Law for Fermions
Wolf, M. M. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.010404 · Cited by 463
Self-citationStructure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality
Hayden, P., Jozsa, R., Petz, D., & Winter, A. (2004) · Communications in Mathematical Physics · doi:10.1007/s00220-004-1049-z · Cited by 429
Entropy, Entanglement, and Area: Analytical Results for Harmonic Lattice Systems
Plenio, M. B., Eisert, J., Dreißig, J., & Cramer, M. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.060503 · Cited by 403
Randomizing Quantum States: Constructions and Applications
Hayden, P., Leung, D., Shor, P. W., & Winter, A. (2004) · Communications in Mathematical Physics · doi:10.1007/s00220-004-1087-6 · Cited by 345
Entanglement and alpha entropies for a massive Dirac field in two dimensions
Casini, H., Fosco, C. D., & Huerta, M. (2005) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2005/07/p07007 · Cited by 293
A sharp continuity estimate for the von Neumann entropy
Audenaert, K. M. R. (2007) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/40/28/s18 · Cited by 286
Structure of states which satisfy strong subadditivity of quantum entropy with equality
Hayden, P. M., Jozsa, R., Petz, D., & Winter, A. (2003) · CERN Document Server (European Organization for Nuclear Research) · Cited by 279
Solving gapped Hamiltonians locally
Hastings, M. B. (2006) · Physical Review B · doi:10.1103/physrevb.73.085115 · Cited by 245
Self-citationEntanglement-area law for general bosonic harmonic lattice systems
Cramer, M., Eisert, J., Plenio, M. B., & Dreißig, J. (2006) · Physical Review A · doi:10.1103/physreva.73.012309 · Cited by 239
Entropy and entanglement in quantum ground states
Hastings, M. B. (2007) · Physical Review B · doi:10.1103/physrevb.76.035114 · Cited by 184
Self-citationSpatial structures and localization of vacuum entanglement in the linear harmonic chain
Botero, A., & Reznik, B. (2004) · Physical Review A · doi:10.1103/physreva.70.052329 · Cited by 152
Bonner, J. C., Blöte, H. W. J., Beck, H., & Muller, G. H. (1981) · Springer series in solid-state sciences · doi:10.1007/978-3-642-81592-8_11 · Cited by 56
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2 of the 37 references couldn’t be matched to a known paper.
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- H. Casini, J. Stat. Mech., 2005, P07007
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Colloquium : Area laws for the entanglement entropy
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Orús, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.06.013 · Cited by 2,255
Verstraete, F., Murg, V., & Cirac, J. I. (2008) · Advances In Physics · doi:10.1080/14789940801912366 · Cited by 1,841
Self-citationEntanglement entropy and conformal field theory
Calabrese, P., & Cardy, J. (2009) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/42/50/504005 · Cited by 1,688
“I (n) A:B does not have all the correct properties to be an entanglement measure (see the review by Amico and Fazio in this special issue [8] for a discussion of various entanglement measures), but it has the fundamental property of satisfying the area law [6, 9], even at finite temperature [10].”
BackgroundBlack holes and the butterfly effect
Shenker, S. H., & Stanford, D. (2014) · Journal of High Energy Physics · doi:10.1007/jhep03(2014)067 · Cited by 1,533
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
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