Pure Math Colloquium

Monday, March 22, 2021 — 4:00 PM EDT

Guillaume Aubrun, Université Claude Bernard Lyon 1

"Entangleability of cones"

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 \otimes x2, where x1 \in C1 and x2 \in C2, while their maximal tensor product is the set of tensors that are positive under all product functionals f1 \otimes 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.

(joint work with Ludovico Lami, Carlos Palazuelos, Martin Plavala ; arXiv:1911.09663)

September 2021

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