Holographic mutual information is monogamous
Open accessAbstract
We identify a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions $A$, $B$, $C$ obey the inequality $I(A\ensuremath{\mathbin:}B\ensuremath{\cup}C)\ensuremath{\ge}I(A\ensuremath{\mathbin:}B)+I(A\ensuremath{\mathbin:}C)$, provided entanglement entropies are given by the Ryu-Takayanagi formula. Inequalities of this type are known as monogamy relations and are characteristic of measures of quantum entanglement. This suggests that correlations in holographic theories arise primarily from entanglement rather than classical correlations. We also show that the Ryu-Takayanagi formula is consistent with all known general inequalities obeyed by the entanglement entropy, including an infinite set recently discovered by Cadney et al.; this constitutes strong evidence in favor of its validity.
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If the bulk entropies obey the monogamy of mutual information, then the dual boundary entropies also obey the same.
“where it was shown that if the bulk entropies obey the monogamy of mutual information [66] then the dual boundary entropies also obey the same.”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [66]
Cites
Ryu, S., & Takayanagi, T. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.181602 · Cited by 4,302 · see citing works
Area Laws in Quantum Systems: Mutual Information and Correlations
Wolf, M. M., Verstraete, F., Hastings, M. B., & Cirac, J. I. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.070502 · Cited by 696 · see citing works
Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
Petz, D. (1986) · Communications in Mathematical Physics · doi:10.1007/bf01212345 · Cited by 333 · see citing works
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Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy
Wall, A. C. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/22/225007 · Cited by 545 · see citing works
Causality & holographic entanglement entropy
Headrick, M., Hubeny, V. E., Lawrence, A., & Rangamani, M. (2014) · Journal of High Energy Physics · doi:10.1007/jhep12(2014)162 · Cited by 418 · see citing works
Self-citationHolographic entanglement entropy from 2d CFT: heavy states and local quenches
Asplund, C. T., Bernamonti, A., Galli, F., & Hartman, T. (2015) · Journal of High Energy Physics · doi:10.1007/jhep02(2015)171 · Cited by 280 · see citing works
Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography
Morrison, I. A. (2014) · Journal of High Energy Physics · doi:10.1007/jhep05(2014)053 · Cited by 111 · see citing works
Holographic spacetime, black holes and quantum error correcting codes: a review
Kibe, T., Mandayam, P., & Mukhopadhyay, A. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-10382-1 · Cited by 44 · see citing works
“These inequalities haven’t been shown to hold when we include quantum corrections via the QES prescription, however exploration in this direction was initiated in [87] where it was shown that if the bulk entropies obey the monogamy of mutual information [64] then the dual boundary entropies also obey the same.”
BackgroundHawking radiation correlations of evaporating black holes in JT gravity
Hollowood, T. J., Kumar, S. P., & Legramandi, A. (2020) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/abbc51 · Cited by 36 · see citing works
Quantum Extremal Surfaces and the Holographic Entropy Cone
Akers, C., Hernández-Cuenca, S., & Rath, P. (2021) · Journal of High Energy Physics · doi:10.1007/jhep11(2021)177 · Cited by 32 · see citing works
- Authors
- Hayden, P., Headrick, M., & Maloney, A.
- Affiliations
- McGill University (CA)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2013-02-06
- Volume
- 87
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2041625524
- Cited by
- 326
- References
- 3
- Citations by year
- 2026: 21 · 2025: 32 · 2024: 27 · 2023: 32 · 2022: 29 · 2021: 25 · 2020: 32 · 2019: 31 · 2018: 27 · 2017: 11 · 2016: 19 · 2015: 18 · 2014: 13 · 2013: 3 · 2012: 4
- FWCI
- 8.06
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy
- Topics
- 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 many-body systems
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- monogamy of entanglement, Ryu-Takayanagi formula, entanglement entropy, quantum entanglement, classical correlations, entanglement inequalities, AdS/CFT correspondence
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