The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Largest separable balls around the maximally mixed bipartite quantum state
Open accessAbstract
For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral ${l}_{p}$ norms for $1<~p<~\ensuremath{\infty},$ of separable (unentangled) matrices around the identity matrix. This implies a simple and intuitively meaningful geometrical sufficient condition for separability of bipartite density matrices: that their purity $\mathrm{tr}{\ensuremath{\rho}}^{2}$ not be too large. Theoretical and experimental applications of these results include algorithmic problems such as computing whether or not a state is entangled, and practical ones such as obtaining information about the existence or nature of entanglement in states reached by nuclear magnetic resonance quantum computation implementations or other experimental situations.
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
Quantum Theory: Concepts and Methods
(2002) · doi:10.1007/0-306-47120-5 · Cited by 1,029
Cited by
Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.865 · Cited by 10,118
The Theory of Quantum Information
Watrous, J. (2018) · doi:10.1017/9781316848142 · Cited by 1,325
Enhancing the Charging Power of Quantum Batteries
Campaioli, F., Pollock, F. A., Binder, F. C., Céleri, L., Goold, J., Vinjanampathy, S., & Modi, K. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.150601 · Cited by 531
Wilde, M. M., Winter, A., & Yang, D. (2014) · Communications in Mathematical Physics · doi:10.1007/s00220-014-2122-x · Cited by 516
Classical deterministic complexity of Edmonds' Problem and quantum entanglement
Gurvits, L. (2003) · Proceedings of the thirty-fifth annual ACM symposium on Theory of computing · doi:10.1145/780542.780545 · Cited by 448
Self-citation
Metadata
- Authors
- Gurvits, L., & Barnum, H.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2002-12-12
- Volume
- 66
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1985426276
- Cited by
- 281
- References
- 1
- FWCI
- 7.03
- Type
- journal article
- Language
- en
- Open access
- green
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: Largest separable balls around the maximally mixed bipartite quantum state. https://app.cochat.ai/papers/10.1103/physreva.66.062311
- The paper
- Gurvits, L., & Barnum, H. (2002). Largest separable balls around the maximally mixed bipartite quantum state. Physical Review A. https://doi.org/10.1103/physreva.66.062311
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.
