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arXiv · 1911.01494

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

Honghao Fu
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Abstract

We show that for any prime odd integer $d$, there exists a correlation of size $Θ(r)$ 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.

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Honghao Fu. 2021-12-27. Constant-sized correlations are sufficient to robustly self-test maximally entangled states with unbounded dimension. https://doi.org/10.22331/q-2022-01-03-614

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