Palazuelos Cabezón, Carlos2024-01-292024-01-292021G. Aubrun, L. Lami, C. Palazuelos, M. Plávala, Entangleability of cones, Geom. Funct. Anal. 31 (2021) 181–205. https://doi.org/10.1007/s00039-021-00565-5.1016-443X10.1007/S00039-021-00565-5https://hdl.handle.net/20.500.14352/95783We solve a long-standing conjecture by Barker, proving 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. Here, given two proper cones , , their minimal tensor product is the cone generated by products of the form , where and , while their maximal tensor product is the set of tensors that are positive under all product functionals , where and . Our proof techniques involve a mix of convex geometry, elementary algebraic topology, and computations inspired by quantum information theory. Our motivation comes from the foundations of physics: as an application, we show that any two non-classical systems modelled by general probabilistic theories can be entangled.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal article1420-8970https://doi.org/10.1007/S00039-021-00565-5restricted accessEntangleabilityGeneral probabilistic theoriesTensor product of conesAnálisis funcional y teoría de operadores1202 Análisis y Análisis Funcional