RT Journal Article
T1 Entangleability of cones
A1 Palazuelos Cabezón, Carlos
AB 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.
PB SpringerLink
SN 1016-443X
YR 2021
FD 2021
LK https://hdl.handle.net/20.500.14352/95783
UL https://hdl.handle.net/20.500.14352/95783
LA eng
NO 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.
NO Alexander von Humboldt Foundation
NO Slovak Research and Development Agency
NO Deutsche Forschungsgemeinschaft
NO European Commission
NO Comunidad de Madrid
NO Ministerio de Economía y Competitividad (España)
DS Docta Complutense
RD 13 jun 2025