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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260505T150000
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URL:https://uwaterloo.ca/pure-mathematics/events/analysis-seminar-217
SUMMARY:Analysis Seminar
CLASS:PUBLIC
DESCRIPTION:PAUL SKOUFRANISYORK UNIVERSITY\n\n_Non-Commutative Majorization
 _\n\nThe maps that send a self-adjoint matrix $A$ to $U^*AU$ where $U$ is 
 a\nunitary matrix are essential inQuantum Information Theory as these\nmap
 s transmit quantum information in a reversible way. When\nconvexcombinatio
 ns of such maps are taken\, one obtains what are known\nas the mixed unita
 ry quantum channels\, whichare essential models for\nhow quantum informati
 on can be transmitted when noise is present. Just\nas the unitaryconjugate
 s of a self-adjoint matrix can be determined\nvia spectral data\, so too c
 an the image of a self-adjointmatrix under\nall possible mixed unitary qua
 ntum channels. Since this is equivalent\nto characterizing the convexhull 
 of the unitary orbit of a\nself-adjoint matrix\, this problem has a well-k
 nown solution from\noperator theoryinvolving the notion of matrix majoriza
 tion of one\nself-adjoint operator by another. In this talk\, we will exam
 inehow we\ncan extend the notion of matrix majorization to non-commutative
 \ncontexts. In particular\, we will discussa notion of non-commutative\nma
 jorization that characterizes the potential outputs under all\nquantum cha
 nnels ofany non-commutative tuple of matrices. This is\nbased on joint wor
 k with Matt Kennedy.\n\nMC 5417 or Join on Zoom\n[https://uwaterloo.zoom.u
 s/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09]
DTSTAMP:20260430T230030Z
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