Interactive Quantum Information Theory: Fundamentals and Applications

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One of the cornerstones of 20th century science was the development of information theory by Claude Shannon. In a single paper, Shannon laid the mathematical foundations for a revolution in communication technology. His two quintessential results, the noiseless and noisy coding theorems, changed forever the way we approach compression and error correction codes. These theorems form the backbone for much of current digital technology, from mobile telephony to file compression and the communication layer of the Internet.******Traditionally, communication is studied in a unidirectional setting, where a sender can wait for an arbitrarily long time to encode a long message; in contrast, with interactive communication, as in a conversation, it is necessary to transmit shorter messages that are not optimal in rate of data communication. Communication complexity is the mathematical theory of such interactive processes, and is one of the core models of computation studied in theoretical computer science. It has multiple practical applications to concrete models of computation such as streaming algorithms and data structures. Recent years have seen a flurry of results in classical interactive information theory, providing extensions of Shannon's results to this interactive communication setting.******In the last decades, extensions of such ideas have been studied in the realm of quantum information processing, for which we try to harness the counter-intuitive laws of nature at the subatomic level in order to process information in fundamentally different ways than what is offered by classical information processing as experienced in our day-to-day lives. The unique properties of quantum information make it intrinsically harder to handle and more susceptible to noise than classical information.******The main goal of the proposed research program is to develop a theory of information for interactive quantum communication protocols, and apply the developed tools to the study of the complexity of computational problems in quantum communication complexity and other concrete models of quantum computation. ******My proposed research program can be split into two broad research themes: the development of interactive quantum analogues to Shannon's compression and error correcting codes. Moreover, we develop applications of the tools created for such an interactive quantum information theory to relevant problems in quantum communication complexity and other concrete models of quantum computing.******One of the main reasons to study quantum information processing is that it leads to qualitative and quantitative advantages over classical information processing, and Canada is a world leader in developing such quantum technology. This is a very promising economical area and my program will also serve towards the formation of talented scientists in this field which is a burgeoning economical sector in Canada, with many young promising companies.