Speaker
Description
We apply information-theoretic de Finetti principles to build convergent approximation schemes with explicit finite-level guarantees, yielding both outer relaxations and certified inner points. For polynomial optimization over convex bodies with local equality and inequality constraints, an information-theoretic monogamy argument yields a convergent conic hierarchy whose approximation error decays as $\mathcal{O}[1/\sqrt{n}]$ with the extension level, resolving the lack of finite-level guarantees for inequality-constrained de Finetti-based methods. A constructive rounding scheme converts outer feasible points into certified interior approximations, producing matching inner/outer bounds that “sandwich” the true optimum. As an application, we express the optimal GPT value of two-player non-local games as a polynomial optimization problem with local constraints, enabling finite-convergence approximation guarantees in the GPT setting. In the quantum setting of fixed-size free games with bounded entanglement assistance, we obtain SDP outer hierarchies with $\varepsilon$-additive guarantees and combine them with measurement-based rounding to generate inner sequences of feasible strategies. Crucially, we achieve overall $\operatorname{poly}[1/ \varepsilon]$ complexity by exploiting representation-theoretic symmetry reduction (symmetric subspace/Bose symmetry, Schur–Weyl duality, block decompositions) to construct the SDPs directly in symmetry-adapted bases. Finally, for approximate quantum error correction under symmetric noise, we round extendability-based outer bounds into explicit encoder–decoder pairs and develop a framework that combines noise symmetries with extendability symmetry (via commuting group actions) to make higher hierarchy levels computationally feasible. The work is based on arXiv:2507.12326, 2507.12302 and 2601.15184.