Heuristic lower bounds on real Grothendieck constants of finite and infinite order

arXiv:2609.35399 · quant-ph · Submitted 2026-09-28 · Read on arXiv

quant-ph

Submitted: 2026-09-28

Updated: 2026-09-28

Terminology

• Consistency — 2× in this paper · explained in 3 episodes
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 4 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Quantum Physics — 1× in this paper · explained in 11 episodes

Sources

• Grothendieck's Theorem, past and present
• Grothendieck's constant and local models for noisy entangled quantum states
• More efficient Bell inequalities for Werner states
• Convex separation from convex optimization for large-scale problems
• Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$
• The Platonic solids and fundamental tests of quantum mechanics
• Classical bounds on two-outcome bipartite Bell expressions and linear prepare-and-measure witnesses: Efficient computation in parallel environments such as graphics processing units
• Improved local models and new Bell inequalities via Frank-Wolfe algorithms
• Better bounds on finite-order Grothendieck constants
• Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements
• Qutrit witness from the Grothendieck constant of order four
• The Grothendieck constant is strictly smaller than Krivine's bound
• An Upper Bound on Grothendieck's Constant
• New Lower and Upper Bounds for the Grothendieck Constant
• A Lower Bound for Grothendieck's Constant
• The Grothendieck Constant is Strictly Larger than Davie-Reeds' Bound
• Beating one bit of communication with and without quantum pseudo-telepathy
• Measurement of areas on a sphere using Fibonacci and latitude-longitude lattices
• Bell nonlocality
• Testing the Hilbert space dimension

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