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SUMMARY:Combinatorial Theory of Matrix Spaces and Its Applications in Quan
 tum Information - Yinan Li
DTSTART:20230719T131500Z
DTEND:20230719T141500Z
UID:TALK202672@talks.cam.ac.uk
CONTACT:Sergii Strelchuk
DESCRIPTION:Duan\, Severini\, and Winter proposed the study of a specific 
 matrix space as a quantum generalization of graphs\, which allows for the 
 formulation and study of a quantum version of Shannon's zero-error capacit
 y problem. In this talk\, we further develop the combinatorial theory of m
 atrix spaces through the lens of graph theory. Initially\, we introduce ba
 sic correspondences between matrix space properties and graph-theoretical 
 properties\, such as nilpotency versus acyclicity\, irreducibility versus 
 connectivity\, and dimension expansion versus vertex expansion. Subsequent
 ly\, we demonstrate how these correspondences can be enhanced to the so-ca
 lled inherited correspondences\, which lead to extremal problems for matri
 x spaces and have applications in invariant theory and noncommutative alge
 bra. Finally\, we discuss applications in quantum information processing a
 nd provide examples of graph-theoretic properties that are no longer valid
  in the matrix space setting.
LOCATION:MR14
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