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SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20251013T123000Z
DTEND:20251013T133000Z
DTSTAMP:20260422T135913Z
UID:BilTop/121
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BilTop/121/"
 >The geometry of simplicial distributions on suspension scenarios</a>\nby 
 Aziz Kharoof (Bilkent University) as part of Bilkent Topology Seminar\n\nL
 ecture held in SA 141.\n\nAbstract\nQuantum measurements often exhibit non
 -classical features\, such as contextuality\, which generalizes Bell's non
 -locality and serves as a resource in various quantum computation models. 
 Existing frameworks have rigorously captured these phenomena\, and recentl
 y\, simplicial distributions have been introduced to deepen this understan
 ding. The geometrical structure of simplicial distributions can be seen as
  a resource for applications in quantum information theory. In this talk\,
  we use topological foundations to study this geometrical structure\, leve
 raging the fact that\, in this simplicial framework\, measurements and out
 comes are represented as spaces. This allows us to depict contextuality as
  a topological phenomenon. We show that applying the cone construction to 
 the measurement space makes the corresponding non-signaling polytope equal
  to the join of m copies of the original polytope\, where m is the number 
 of possible outcomes per measurement. Then we glue two copies of cone meas
 urement spaces to obtain a suspension measurement space. The decomposition
  done for simplicial distributions on a cone measurement space provides de
 eper insights into the geometry of simplicial distributions on a suspensio
 n measurement space and aids in characterizing the contextuality there. Ad
 ditionally\, we apply these results to derive a new type of Bell inequalit
 ies (inequalities that determine the set of local joint probabilities/non-
 contextual simplicial distributions) and to offer a mathematical explanati
 on for certain contextual vertices from the literature.\n
LOCATION:https://researchseminars.org/talk/BilTop/121/
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