2026-06-29T16:40:31Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/957832025-03-25T00:54:49Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Palazuelos Cabezón, Carlos author 2021 We 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. G. 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. 1016-443X 10.1007/S00039-021-00565-5 https://hdl.handle.net/20.500.14352/95783 1420-8970 https://doi.org/10.1007/S00039-021-00565-5 Entangleability of cones