Proof of the strong subadditivity of quantum-mechanical entropy
Abstract
We prove several theorems about quantum-mechanical entropy, in particular, that it is strongly subadditive.
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Strong subadditivity means that a single system cannot be strongly entangled with two different systems at once.
“However, strong sub-additivity means that a single system cannot be strongly entangled with two different systems at once [11].”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [11]
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- Authors
- Lieb, E. H., & Ruskai, M. B.
- Affiliations
- I.H.E.S., 91 Bures-sur-Yvette, France
- Massachusetts Institute of Technology (US)
- ORCID
- Ruskai, Mary Beth
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1973-12-01
- Volume
- 14
- Issue
- 12
- Pages
- 1938-1941
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2105918132
- Cited by
- 831
- References
- 0
- Citations by year
- 2026: 22 · 2025: 45 · 2024: 42 · 2023: 53 · 2022: 38 · 2021: 39 · 2020: 45 · 2019: 37 · 2018: 45 · 2017: 42 · 2016: 57 · 2015: 46 · 2014: 49 · 2013: 38 · 2012: 21
- FWCI
- 4.44
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Mathematical Physics (publishedVersion)
- French digital mathematics library (Numdam) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- strong subadditivity, quantum entropy, von Neumann entropy, quantum information, entropy inequality
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