Graduate Seminar

Location:  CL 317 and Livestream

Speaker: Mahbuba Rahman

MSc Student supervised by Michael Kozdron

Title:  Quantum Probability and a Quantum Bayes' Rule on an Infinite-dimensional Hilbert Space

Zoom: https://uregina-ca.zoom.us/j/92053635111?pwd=U25NcEp6amlGV1YrRDdnUm5qNlhaUT09

Abstract:

In this talk we will consider a normalised positive operator valued measure (POVM) on an infinite-dimensional Hilbert space to measure a quantum system. To construct the mathematical formulation of the quantum measurement, the states of the quantum system are modelled by full rank density operators on an infinite-dimensional Hilbert space. Farenick, Plosker, Smith (2011) and Farenick, Kozdron (2012) generalized classical limiting results to the quantum setting. In the classical setting, the Radon-Nikodym theorem is fundamental for proving existence of conditional expectation in probability. Farenick and Kozdron (2012) used the non-principal Radon-Nikod´ym derivative to construct a quantum conditional expectation and proved a quantum version of Bayes’ rule.

All of the aforementioned work was done for a finite-dimensional Hilbert space. McLaren, Plosker and Ramsey (2020) defined a Radon-Nikodym derivative for an infinite-dimensional Hilbert space. Building on that work, in this talk we made necessary changes to extend those results to prove a quantum version of Bayes' rule on an infinite-dimensional Hilbert space.