Prairie Mathematics Colloquium: Michael Kozdron

  • Date: 03/09/2023
Michael Kozdron, University of Regina

University of Regina


A Quantum Martingale Convergence Theorem


It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. A quantum probability is a normalised POVM, namely a function on certain subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a probability and whose values are positive operators acting on a complex Hilbert space. A quantum random variable is an operator valued function which is measurable with respect to a quantum probability.


In this talk, we will discuss a quantum analogue of the classic Lebesgue dominated convergence theorem and use it to prove a quantum martingale convergence theorem (MCT). In contrast with the classical MCT, the quantum MCT exhibits non-classical behaviour; even though the limit of the martingale exists and is unique, it is not explicitly identifiable. Fortunately, a partial classification of the limit is possible through a study of the space of all quantum random variables having quantum expectation zero. Based on joint work with Kyler Johnson. Note that this general audience talk will assume only a basic understanding of undergraduate probability and graduate real analysis (i.e., Lebesgue integration).


This event is part of the Prairie Mathematics Colloquium.


Other Information: 

Location: Live Stream. Join with Zoom link.


More details listed here.


Time: Social tea break at 2pm Central, Talk at 2.30pm Central.