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Mathematics Seminar Date: Wednesday, 20 November 2024 Time: 03:30 PM Venue: Seminar Hall, CMI Probabilistic Foundations and Applications in Quantum Information Theory Tiju Cherian John University of Arizona. 20-11-24 Abstract Classical information theory, grounded in probability theory, has provided the theoretical framework that led to the development of moderncommunication systems like wireless networks and the internet. Similarly,quantum information theory, rooted in quantum probability (ornoncommutative probability), holds transformative potential for futuretechnologies. A recent solution to a conjecture by K. R. Parthasarathy hasestablished a quantum probability analogue to the foundational idea of ???probability measures on Hilbert spaces.??? Much like classical probability???simpact on other areas of mathematics, this quantum framework opens new avenues, including symplectic spectral theory and quantum theory on analytic function spaces. After outlining these developments, we answer a long-standing question in quantum information theory and address a conjecture by Seshadreesan, Lami, and Wilde on quantum entropy. Additionally, a related mathematical discovery has achieved a fourfold improvement in detecting transmission loss, with promising implications for communication technologies. We conclude by exploring recent findings and open problems on the monotonicity of quantum entropy within the frameworkof quantum central limit theorems.
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