The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
The proper formula for relative entropy and its asymptotics in quantum probability
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
On Information and Sufficiency
Kullback, S., & Leibler, R. A. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729694 · Cited by 20,193
Quantum detection and estimation theory
Helstrom, C. W. (1969) · Journal of Statistical Physics · doi:10.1007/bf01007479 · Cited by 3,776
Information Theory: Coding Theorems for Discrete Memoryless Systems
Csiszár, I., & Körner, J. (2014) · REAL-EOD (Library of the Hungarian Academy of Sciences and the Information Center Oriental Collection) · Cited by 3,246
Quantum Detection and Estimation Theory
(1976) · Mathematics in Science and Engineering · doi:10.1016/s0076-5392(08)x6017-5 · Cited by 2,426
Entropy, Large Deviations, and Statistical Mechanics
Ellis, R. S. (1985) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-1-4613-8533-2 · Cited by 1,196
Entropy, Large Deviations, and Statistical Mechanics
Ellis, R. S. (2006) · Classics in Mathematics · doi:10.1007/3-540-29060-5 · Cited by 1,134
Ergodic Theory and Information
S., D., & Billingsley, P. (1966) · Mathematics of Computation · doi:10.2307/2003618 · Cited by 1,070
Principles and practice of information theory
Blahut, R. E. (1987) · Medical Entomology and Zoology · Cited by 1,008
Ergodic Theory and Information
Révész, P., Billingsley, P., & Revesz, P. (1966) · Revue de l'Institut International de Statistique / Review of the International Statistical Institute · doi:10.2307/1401263 · Cited by 864
Ergodic Theory and Information.
Kingman, J. F. C., & Billingsley, P. (1966) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2343508 · Cited by 779
Cited by
Entanglement measures and purification procedures
Vedral, V., & Plenio, M. B. (1998) · Physical Review A · doi:10.1103/physreva.57.1619 · Cited by 1,419
A Fully Quantum Asymptotic Equipartition Property
Tomamichel, M., Colbeck, R., & Renner, R. (2009) · IEEE Transactions on Information Theory · doi:10.1109/tit.2009.2032797 · Cited by 356
A Survey on Quantum Channel Capacities
Gyongyosi, L., Imre, S., & Nguyen, H. V. (2018) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2017.2786748 · Cited by 337
Entanglement theory and the second law of thermodynamics
Brandão, F. G. S. L., & Plenio, M. B. (2008) · Nature Physics · doi:10.1038/nphys1100 · Cited by 189
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
“The result of Hiai and Petz is that [108]:”
Background
Metadata
- Authors
- Hiai, F., & Petz, D.
- Venue
- Communications in Mathematical Physics
- Published
- 1991-12
- Volume
- 143
- Issue
- 1
- Pages
- 99-114
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W1968087916
- Cited by
- 522
- References
- 25
- FWCI
- 1.14
- Type
- journal article
- Language
- en
- Open access
- closed
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 ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: The proper formula for relative entropy and its asymptotics in quantum probability. https://app.cochat.ai/papers/10.1007/bf02100287
- The paper
- Hiai, F., & Petz, D. (1991). The proper formula for relative entropy and its asymptotics in quantum probability. Communications in Mathematical Physics. https://doi.org/10.1007/bf02100287
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
