01123nas a2200133 4500008004100000245012100041210006900162260001500231300000800246490000600254520067600260100001600936856003700952 2022 eng d00aConstant-sized correlations are sufficient to robustly self-test maximally entangled states with unbounded dimension0 aConstantsized correlations are sufficient to robustly selftest m c01/03/2022 a6140 v63 a
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 Z∗d. 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.
1 aFu, Honghao uhttps://arxiv.org/abs/1911.01494