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].
“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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- 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 › Computer Science › Artificial Intelligence › 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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