MARCH 9, 2023

SPEAKER:

Michael Kozdron, Associate Professor at the University of Regina in the Department of Mathematics and Statistics

(Learn more about the speaker here)

TITLE: "A Quantum Martingale Convergence Theorem"

ABSTRACT: 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).

TIME: All in The Central Time Zone

Meet and Greet:

2:00pm-2:30pm CST

Talk:

2:30pm-3:20pm CST

Questions:

3:20pm-3:30pm CST

LOCATION:

The event will take place via Zoom

Zoom Meeting Details:

ZOOM LINK: https://umanitoba.zoom.us/j/66893629644?pwd=MGNWdjlZZXk2U29vWFMwVHMzYjlQUT09

Meeting ID: 668 9362 9644

Passcode: 355598