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

We show that for any prime odd integer \(d\), there exists a correlation of size \(\Theta(r)\) that can robustly self-test a maximally entangled state of dimension \(4d-4\), where \(r\) is the smallest multiplicative generator of \(\mathbb{Z}_d^\ast\). The construction of the correlation uses the em...

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Bibliographic Details
Published inarXiv.org
Main Author Fu, Honghao
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.12.2021
Subjects
Correlation
Entangled states
Physics - Quantum Physics
Prime numbers
Robustness (mathematics)
Self testing
Self tests
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Summary:We show that for any prime odd integer \(d\), there exists a correlation of size \(\Theta(r)\) that can robustly self-test a maximally entangled state of dimension \(4d-4\), where \(r\) is the smallest multiplicative generator of \(\mathbb{Z}_d^\ast\). The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. Vol. \(7\), (\(2019\))). Since there are infinitely many prime numbers whose smallest multiplicative generator is at most \(5\) (M. Murty The Mathematical Intelligencer \(10.4\) (\(1988\))), our result implies that constant-sized correlations are sufficient for robust self-testing of maximally entangled states with unbounded local dimension.
ISSN:2331-8422
DOI:10.48550/arxiv.1911.01494