Better Bounds on Grothendieck Constants of Finite Orders

Watch a 57-minute research seminar where Sébastien Designolle from Zuse Institute Berlin explores improved bounds on Grothendieck constants of finite orders. Dive into the mathematical analysis of K_G(d) constants, which measure the advantage of d-dimensional strategies over 1-dimensional approaches in optimization tasks, with applications in approximation algorithms and quantum nonlocality. Learn about a novel Frank-Wolfe approach for establishing lower bounds, particularly for dimensions d=3,4,5, where specific rectangular instances provide certified improvements over previous known bounds. Explore the construction of highly symmetric instances for d=4,7,8 that suggest even better bounds through heuristic solutions. Understand the relationship between these constants and Bell inequality violations, including an interpretation of generalized constants K_G(d→2) as the advantage of complex quantum mechanics over real quantum mechanics. Part of the Quantum Information and Quantum Computing Seminars series at Centrum Fizyki Teoretycznej PAN.