Tuesday, December 21 2021
15:30 - 16:45

IMSc Webinar

Fundamental Performance Limits and New Strategies in Quantum Information Theory, Communication and Learning

Arun Padakandla

University of Tennessee at Knoxville

In this talk, I will describe my findings on two problems in Quantum Information and Quantum Learning. In the first part, I consider the problem of quantifying the amount of information contained in the outcome of a quantum measurement. Since the outcome of a quantum measurement is inherently random, it is natural to enquire how much intrinsic information of the particle being measured does the outcome contain. Adopting an information-theoretic formulation I address this problem in network scenarios involving multiple centralized/distributed measurements. I derive lower bounds on the amount of information in terms of Holevo information quantities. In the second part of my talk, I formulate a problem of learning from data encoded on quantum states. Consider a universe consisting of a set of quantum states, with each state being assigned one among a set of labels. The goal of a learning algorithm is to decipher the underlying relationship between the states and the labels. Motivating this problem from both statistical learning as well as quantum physics, we formulate a quantum analogue of the fundamental classical PAC learning problem. We propose and analyze a new quantum empirical risk minimization algorithm and derive sample complexity bounds. In the last part of my talk, I present an overview of my results in quantum and classical communication and indicate new connections between classical information theory and certain decidability problems being currently studied in theoretical computer science. My talk will focus on illustrating the ideas to a broad audience and will be accessible to all.

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