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Semidefinite Block-Matrix Relaxations for Computing Quantum Correlations

D' Alessandro, Nicola LU orcid ; Roch I Carceller, Carles LU orcid and Tavakoli, Armin LU (2026) In Physical Review X 16(3).
Abstract

Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today’s leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant types of constraints. Here, we propose a general semidefinite relaxation methodology that can incorporate a breadth of constraints needed in various quantum correlation problems, thereby generalising the seminal Navascués-Pironio-Acín hierarchy. It yields useful results at reasonable computational cost. We showcase the methodology and its features by using it to address five different quantum information problems. These are (i) entanglement witnessing from imperfect measurement devices, (ii) certifying... (More)

Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today’s leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant types of constraints. Here, we propose a general semidefinite relaxation methodology that can incorporate a breadth of constraints needed in various quantum correlation problems, thereby generalising the seminal Navascués-Pironio-Acín hierarchy. It yields useful results at reasonable computational cost. We showcase the methodology and its features by using it to address five different quantum information problems. These are (i) entanglement witnessing from imperfect measurement devices, (ii) certifying measurements from fidelity-constrained sources, (iii) computing dimensionality in genuine multiparticle entangled states, (iv) benchmarking dimensionality for state preparation devices, and (v) finding uncertainty relations for nearly anticommuting observables. These applications reflect both the usefulness and versatility of the methodology, as well as its potential for broader relevance in the field.

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publishing date
type
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publication status
published
subject
in
Physical Review X
volume
16
issue
3
article number
031050
publisher
American Physical Society
external identifiers
  • scopus:105048333094
ISSN
2160-3308
DOI
10.1103/6rh2-s3y2
language
English
LU publication?
yes
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Publisher Copyright: Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.
id
d21279a2-de0d-4159-8d0e-f9d337407d51
date added to LUP
2026-09-10 13:43:25
date last changed
2026-09-14 14:34:43
@article{d21279a2-de0d-4159-8d0e-f9d337407d51,
  abstract     = {{<p>Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today’s leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant types of constraints. Here, we propose a general semidefinite relaxation methodology that can incorporate a breadth of constraints needed in various quantum correlation problems, thereby generalising the seminal Navascués-Pironio-Acín hierarchy. It yields useful results at reasonable computational cost. We showcase the methodology and its features by using it to address five different quantum information problems. These are (i) entanglement witnessing from imperfect measurement devices, (ii) certifying measurements from fidelity-constrained sources, (iii) computing dimensionality in genuine multiparticle entangled states, (iv) benchmarking dimensionality for state preparation devices, and (v) finding uncertainty relations for nearly anticommuting observables. These applications reflect both the usefulness and versatility of the methodology, as well as its potential for broader relevance in the field.</p>}},
  author       = {{D' Alessandro, Nicola and Roch I Carceller, Carles and Tavakoli, Armin}},
  issn         = {{2160-3308}},
  language     = {{eng}},
  month        = {{07}},
  number       = {{3}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review X}},
  title        = {{Semidefinite Block-Matrix Relaxations for Computing Quantum Correlations}},
  url          = {{http://dx.doi.org/10.1103/6rh2-s3y2}},
  doi          = {{10.1103/6rh2-s3y2}},
  volume       = {{16}},
  year         = {{2026}},
}