Papers › Entangleability of cones
Entangleability of cones
Guillaume Aubrun, Ludovico Lami, Carlos Palazuelos, Martin Plavala
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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 C₁, C₂, their minimal tensor product is the cone generated by products of the form x₁ ⊗x₂, where x₁ ∈C₁ and x₂ ∈C₂, while their maximal tensor product is the set of tensors that are positive under all product functionals f₁ ⊗f₂, where f₁ is positive on C₁ and f₂ is positive on C₂. 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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