Information can be captured as a measure of how far a probability space is away from being a "sure thing", or equivalently, how much data is required to uniquely specify an event. A fair coin flip contains more information than an unbalanced coin. As the coin becomes more and more biased, a flip tends towards having no informational content. Classically, this leads to a rich theory including an analysis of the efficiency of encodings, compressions, and transmissions of information. It is exactly "A Mathematical Theory of Communication".
Information becomes quantum when it starts being contextual and linear. Essentially, we cannot assign all events in the quantum event lattice consistent probabilities and information cannot be duplicated or destroyed. The theme for this semester's mathematical physics seminars is Quantum Information, and this first talk serves as an introduction to the foundations. We will compare the basic ingredients of quantum information theory to the classical counterpart, in particular their event structures and their notions of entropy.
Over the course of the semester, we will cover such topics as decoherence in communication channels, distinguishing quantum states, information geometry, and the topological model of quantum computing. We aim to enhance our understanding by utilizing the duality between the boolean logic of subsets and the partition logic of quotients used respectively in probability and information theory, and to express these through a unifying sheaf theoretic formalism.
Information, Classical and Quantum: An Introduction
Feb. 09, 2022 4pm (Math 350)
Math Club
organized by Agnes Beaudry and Jonathan Quartin (Diversity Committee)
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What's undergraduate math research anyways? Who is it for? It might not be what you think it's like and it might be for you, even if you haven't realized it yet! So come to the Math Club on Wednesday Feb 2 from 4 - 5 pm to learn more about undergraduate math research and the opportunities for math research experiences available to CU undergrads. And if you're wondering, does math research happen online? The answer is absolutely!
Information, Classical and Quantum: An Introduction