Recorded Seminars

 

Speaker: Professor Paul Skoufranis (York University)

Title: Linear Algebra, Quantum Information Theory, and Operator Algebras

Abstract: Linear algebra has many connections to a wide variety of areas of mathematics, science, and technology.  One of the more recent connections is Quantum Information Theory where the states of quantum systems are studied.  In Quantum Information Theory, a quantum channel is a communication channel that can transmit quantum information such as a qubit.  More mathematically precise, a quantum channel is a trace-preserving, completely positive map between spaces of operators, such as the collection of n by n matrices.  In this talk, we will discuss linear algebra and its generalizations in relation to quantum information theory.  To be specific, we will examine the general behaviour of trace-preserving, completely positive maps on matrices and analyze a few specific examples.  Through these examples, some interesting structural results on the n by n matrices will be observed.  Finally, we will consider how this theory generalizes to infinite dimensions through the lens of Operator Algebras.

Video: Video Link

Slides: Slides Link

 

 

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