Constant-sized correlations are sufficient to robustly self-test 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 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.

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

References in corpus (5)

• Robust Self Testing of the Singlet
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• MIP*=RE
• Biased nonlocal quantum games
• Constant-sized robust self-tests for states and measurements of unbounded dimension

Cited by in corpus (6)

• Almost synchronous quantum correlations
• All Real Projective Measurements Can be Self-tested
• Constant-sized self-tests for maximally entangled states and single projective measurements
• Practical parallel self-testing of Bell states via magic rectangles
• Parallel remote state preparation for fully device-independent verifiable blind quantum computation
• The membership problem for constant-sized quantum correlations is undecidable