Catherine St-Pierre, University of Waterloo
Organizational meeting
We will organize the seminars for the summer.
MC 5403
Paul SkoufranisYork University
Non-Commutative Majorization
The maps that send a self-adjoint matrix $A$ to $U^*AU$ where $U$ is a unitary matrix are essential inQuantum Information Theory as these maps transmit quantum information in a reversible way. When convexcombinations of such maps are taken, one obtains what are known as the mixed unitary quantum channels, whichare essential models for how quantum information can be transmitted when noise is present. Just as the unitaryconjugates of a self-adjoint matrix can be determined via spectral data, so too can the image of a self-adjointmatrix under all possible mixed unitary quantum channels. Since this is equivalent to characterizing the convexhull of the unitary orbit of a self-adjoint matrix, this problem has a well-known solution from operator theoryinvolving the notion of matrix majorization of one self-adjoint operator by another. In this talk, we will examinehow we can extend the notion of matrix majorization to non-commutative contexts. In particular, we will discussa notion of non-commutative majorization that characterizes the potential outputs under all quantum channels ofany non-commutative tuple of matrices. This is based on joint work with Matt Kennedy.
MC 5417 or Join on Zoom