The DOI matches its Crossref record; 38 of the 38 references it cites were found in a registry or an index.
A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
Open accessAbstract
We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work (Navascués et al 2007 Phys. Rev. Lett. 98 010401), we introduced an infinite hierarchy of conditions necessarily satisfied by any set of quantum correlations. Each of these conditions could be tested using semidefinite programming. We present here new results concerning this hierarchy. We prove in particular that it is complete, in the sense that any set of correlations satisfying every condition in the hierarchy has a quantum representation in terms of commuting measurements. Although our tests are conceived to rule out non-quantum correlations, and can in principle certify that a set of correlations is quantum only in the asymptotic limit where all tests are satisfied, we show that in some cases it is possible to conclude that a given set of correlations is quantum after performing only a finite number of tests. We provide a criterion to detect when such a situation arises, and we explain how to reconstruct the quantum states and measurement operators reproducing the given correlations. Finally, we present several applications of our approach. We use it in particular to bound the quantum violation of various Bell inequalities.
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
Horn, R. A., & Johnson, C. R. (1985) · Cited by 22,203
Quantum Computation and Quantum Information
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 18,842
Rudin, W. (1973) · Cited by 13,740
On the Einstein Podolsky Rosen paradox
Bell, J. S. (1964) · Physics Physique Fizika · doi:10.1103/physicsphysiquefizika.1.195 · Cited by 12,252
YALMIP : a toolbox for modeling and optimization in MATLAB
Lofberg, J. (2005) · 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508) · doi:10.1109/cacsd.2004.1393890 · Cited by 9,149
Proposed Experiment to Test Local Hidden-Variable Theories
Clauser, J. F., Horne, M. A., Shimony, A., & Holt, R. A. (1969) · Physical Review Letters · doi:10.1103/physrevlett.23.880 · Cited by 7,573
Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
Sturm, J. F. (1999) · Optimization Methods and Software · doi:10.1080/10556789908805766 · Cited by 7,377
Vandenberghe, L., & Boyd, S. (1996) · SIAM Review · doi:10.1137/1038003 · Cited by 4,105
Global Optimization with Polynomials and the Problem of Moments
Lasserre, J. B. (2001) · SIAM Journal on Optimization · doi:10.1137/s1052623400366802 · Cited by 2,474
Research works printed but not linked: 4
- Tsirelson B, 1993, Had. J. Suppl., 8, 329
- Cirelson B S, 1980, Lett. Math. Phys., 4, 83
- Summers S J, 1988, Ann. Inst. H. Poincaré, 49, 215
- 10.1109/TAC.2005.863494 · doi:10.1109/tac.2005.863494
Cited by
Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., & Wehner, S. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.419 · Cited by 2,688
Self-citationAdvances in quantum cryptography
Pirandola, S., Andersen, U. L., Banchi, L., Berta, M., Bunandar, D., Colbeck, R., Englund, D., Gehring, T., Lupo, C., Ottaviani, C., et al. (2020) · Advances in Optics and Photonics · doi:10.1364/aop.361502 · Cited by 2,033
Random numbers certified by Bell’s theorem
Pironio, S., Acín, A., Massar, S., de la Giroday, A. B., Matsukevich, D. N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T. A., et al. (2010) · Nature · doi:10.1038/nature09008 · Cited by 1,420
Self-citationNonlocality and communication complexity
Buhrman, H., Cleve, R., Massar, S., & de Wolf, R. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.665 · Cited by 622
Self-testing of quantum systems: a review
Šupić, I., & Bowles, J. (2020) · Quantum · doi:10.22331/q-2020-09-30-337 · Cited by 365
Metadata
- Authors
- Navascués, M., Pironio, S., & Acín, A.
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2008-07-08
- Volume
- 10
- Issue
- 7
- Pages
- 073013
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W2162178369
- Cited by
- 721
- References
- 38
- FWCI
- 11.22
- Type
- journal article
- Language
- en
- Open access
- gold
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: A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations. https://app.cochat.ai/papers/10.1088/1367-2630/10/7/073013
- The paper
- Navascués, M., Pironio, S., & Acín, A. (2008). A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations. New Journal of Physics. https://doi.org/10.1088/1367-2630/10/7/073013
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.
