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UID:6149@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220211T143000
DTEND;TZID=Europe/Paris:20220211T153000
DTSTAMP:20241120T200922Z
URL:https://www.i2m.univ-amu.fr/evenements/entangleability-of-cones/
SUMMARY:Guillaume AUBRUN (ICJ\, Université Claude Bernard Lyon 1): Entangl
 eability of cones
DESCRIPTION:Guillaume AUBRUN: We solve a long-standing conjecture by Barker
 \, proving that the minimal and maximal tensor products of two finite-dime
 nsional proper cones coincide if and only if one of the two cones is gener
 ated by a linearly independent set. Here\, given two proper cones C1\, C2\
 , their minimal tensor product is the cone generated by products of the fo
 rm 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 f
 unctionals f1 \\in f2\, where f1 is positive on C1 and f2 is positive on C
 2. Our proof techniques involve a mix of convex geometry\, elementary alge
 braic 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 probabilist
 ic theories can be entangled.\n(arXiv:1911.09663\, joint with Ludovico Lam
 i\, Carlos Palazuelos\, Martin Plavala)
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/12/Guillaume_Aubrun.jpg
CATEGORIES:Séminaire,Signal et Apprentissage
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