# Prairie Mathematics Colloquium

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Thu., Mar. 9, 2023 2:30 p.m.
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Location: Live Stream
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**Time: **Social tea break at 2:00 p.m., Talk at 2:30 p.m.

**Speaker: **Michael Kozdron, University of Regina

**Title: **A Quantum Martingale Convergence Theorem (116 kB)

**Zoom Link: **https://umanitoba.zoom.us/j/66893629644?pwd=MGNWdjlZZXk2U29vWFMwVHMzYjlQUT09

**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).

See: Prairie Mathematics Colloquium

This event is supported by PIMS.