[challenge]: Automated robust self-testing with certified constants

Released by

Jie Wang (AMSS, Chinese Academy of Sciences) & Jin-Guo Liu (Hong Kong University of Science and Technology (Guangzhou))

Contact email

cacate0129@gmail.com

Method

Other

Challenge issue

Difficulty: ★★ (rated by Jie Wang)

Background

Self-testing underpins device-independent cryptography, yet every robustness constant in the literature is hand-derived for one Bell inequality at a time (review: arXiv:2307.02551). The ingredients for automation exist: moment-matrix uniqueness at finite hierarchy level, rounding theory (arXiv:2203.02525), and quantitative stability (arXiv:2204.07084, arXiv:2505.22309).

Research objective

A pipeline that takes a Bell functional and outputs a certified statement — any strategy within ε of the optimal value is O(√ε)-close to the reference strategy — with explicit certified constants derived from strong duality + flatness margins, the perturbation lemmas supplied by the stability theory.

Verification plan

• Success gate: on the catalogue of analytically self-tested inequalities (CHSH, tilted families, CGLMP), the automated constants are valid — never smaller than an adversarially found perturbed strategy allows (validity is attacked, not assumed) — and within a stated factor of the hand-derived ones.
• Hope signal: valid but 100× weaker constants — the pipeline still covers inequalities with no known analytic constant; tighten iteratively.
• Pivot signal: adversarial search finds a strategy violating an emitted constant — the duality step is unsound; the gate design makes this loud.

Why this may lead to research output

Certified automation would industrialize DI security proofs: constants that today take a PhD chapter would take a solver run.

References

1. Tavakoli et al., Semidefinite programming relaxations for quantum correlations, arXiv:2307.02551.
2. Paddock et al., Rounding near-optimal quantum strategies, arXiv:2203.02525.
3. de la Salle, Spectral gap and stability for groups and non-local games, arXiv:2204.07084.
4. Xu et al., Quantitative Tsirelson's theorems, arXiv:2505.22309.

No files, tests, or entry points are identified in the issue. Start by reviewing the cited stability, rounding, and semidefinite-programming references, then inspect the repository for any existing Bell-functional or solver infrastructure. Done means an automated pipeline validates constants against CHSH, tilted families, and CGLMP, with stated comparison or failure results.