Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension

Honghao Fu

doi:10.22331/q-2022-01-03-614

Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension

Honghao Fu

Joint Center for Quantum Information and Computer Science, Institute for Advanced Computer Studies and Department of Computer Science, University of Maryland, College Park, MD 20742, USA

Published:	2022-01-03, volume 6, page 614
Eprint:	arXiv:1911.01494v3
Doi:	https://doi.org/10.22331/q-2022-01-03-614
Citation:	Quantum 6, 614 (2022).

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Abstract

Let $p$ be an odd prime and let $r$ be the smallest generator of the multiplicative group $\mathbb{Z}_p^\ast$. We show that there exists a correlation of size $\Theta(r^2)$ that self-tests a maximally entangled state of local dimension $p-1$. The construction of the correlation uses the embedding procedure proposed by Slofstra ($\textit{Forum of Mathematics, Pi.}$ ($2019$)). Since there are infinitely many prime numbers whose smallest multiplicative generator is in the set $\{2,3,5\}$ (D.R. Heath-Brown $\textit{The Quarterly Journal of Mathematics}$ ($1986$) and M. Murty $\textit{The Mathematical Intelligencer}$ ($1988$)), our result implies that constant-sized correlations are sufficient for self-testing of maximally entangled states with unbounded local dimension.

► BibTeX data

@article{Fu2022constantsized,
  doi = {10.22331/q-2022-01-03-614},
  url = {https://doi.org/10.22331/q-2022-01-03-614},
  title = {Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension},
  author = {Fu, Honghao},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {614},
  month = jan,
  year = {2022}
}

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Cited by

[1] Ranyiliu Chen, Laura Mančinska, and Jurij Volčič, "All real projective measurements can be self-tested", Nature Physics (2024).

[2] Sean A. Adamson and Petros Wallden, "Practical parallel self-testing of Bell states via magic rectangles", Physical Review A 105 3, 032456 (2022).

[3] Thomas Vidick, "Almost synchronous quantum correlations", Journal of Mathematical Physics 63 2, 022201 (2022).

[4] Jurij Volčič, "Constant-sized self-tests for maximally entangled states and single projective measurements", Quantum 8, 1292 (2024).

[5] Anand Natarajan and Tina Zhang, Proceedings of the 55th Annual ACM Symposium on Theory of Computing 1603 (2023) ISBN:9781450399135.

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[7] Harshank Shrotriya, Kishor Bharti, and Leong-Chuan Kwek, "Robust semi-device-independent certification of all pure bipartite maximally entangled states via quantum steering", Physical Review Research 3 3, 033093 (2021).

[8] Zhengfeng Ji, Debbie Leung, and Thomas Vidick, "A three-player coherent state embezzlement game", arXiv:1802.04926, (2018).

[9] Anand Natarajan and Tina Zhang, "Quantum free games", arXiv:2302.04322, (2023).

[10] Honghao Fu, "Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension", Quantum 6, 614 (2022).

[11] Zhengfeng Ji, Debbie Leung, and Thomas Vidick, "A three-player coherent state embezzlement game", Quantum 4, 349 (2020).

The above citations are from Crossref's cited-by service (last updated successfully 2024-09-08 05:14:15) and SAO/NASA ADS (last updated successfully 2024-09-08 05:14:15). The list may be incomplete as not all publishers provide suitable and complete citation data.

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