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A Fully Quantum Asymptotic Equipartition Property
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The classical asymptotic equipartition property is the statement that, in the limit of a large number of identical repetitions of a random experiment, the output sequence is virtually certain to come from the typical set, each member of which is almost equally likely. In this paper, a fully quantum generalization of this property is shown, where both the output of the experiment and side information are quantum. An explicit bound on the convergence is given, which is independent of the dimensionality of the side information. This naturally leads to a family of REacutenyi-like quantum conditional entropies, for which the von Neumann entropy emerges as a special case.
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“Since the reduced density matrix of the entangled state on H 2 consists of a large number of approximately independently and identically distributed thermal modes, the smooth max entropy of H 2 in the entangled state is approximately equal to its von Neumann entropy 2δS BH , up to subleading corrections of order O( √ S) [66].”
From Entanglement wedge reconstruction and the information paradox (2020) · cites this paper as [66]
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Metadata
- Authors
- Tomamichel, M., Colbeck, R., & Renner, R.
- Affiliations
- ETH Zurich (CH)
- Venue
- IEEE Transactions on Information Theory
- Published
- 2009-12
- Volume
- 55
- Issue
- 12
- Pages
- 5840-5847
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2144277460
- Cited by
- 356
- References
- 14
- Citations by year
- 2026: 20 · 2025: 16 · 2024: 21 · 2023: 19 · 2022: 17 · 2021: 30 · 2020: 30 · 2019: 23 · 2018: 26 · 2017: 19 · 2016: 20 · 2015: 20 · 2014: 19 · 2013: 27 · 2012: 19
- FWCI
- 17.68
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Transactions on Information Theory (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Keywords
- typical sets, quantum conditional entropy, von Neumann entropy, side information, convergence bounds, quantum information
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