%0 Journal Article
%A Palazuelos Cabezón, Carlos
%T Entangleability of cones
%D 2021
%@ 1016-443X
%U https://hdl.handle.net/20.500.14352/95783
%X 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.
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