Entangleability of Cones

Explore a groundbreaking lecture on the entangleability of cones presented by Guillaume Aubrun from Institut Camille Jordan, Lyon at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the solution of a long-standing conjecture by Barker, which proves that the minimal and maximal tensor products of two finite-dimensional proper cones coincide if and only if one of the two cones is generated by a linearly independent set. Examine the definitions of minimal and maximal tensor products for proper cones C1 and C2, and discover how the proof techniques combine convex geometry, elementary algebraic topology, and computations inspired by quantum information theory. Understand the implications of this research for the foundations of physics, particularly how it demonstrates that any two non-classical systems modelled by general probabilistic theories can be entangled. Gain insights from this 1-hour 7-minute presentation that bridges mathematics and physics, offering a deeper understanding of entanglement in quantum systems.