Constantsized correlations are sufficient to robustly selftest maximally entangled states with unbounded dimension
Abstract
We show that for any prime odd integer $d$, there exists a correlation of size $\Theta(r)$ that can robustly selftest a maximally entangled state of dimension $4d4$, 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 constantsized correlations are sufficient for robust selftesting of maximally entangled states with unbounded local dimension.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.01494
 Bibcode:
 2019arXiv191101494F
 Keywords:

 Quantum Physics
 EPrint:
 44 pages + 6 pages of supplementary material, 2 figures. v2: fixed typos. v3: published version, focused on the exact case and the robustness analysis can be found in v2