CAREER: A High-Level Framework for a Unified Treatment of Quantum and Classical Information Theory and Thermodynamics

University Of Southern California, Los Angeles CA

Investigators

Abstract

Quantum information theory, a branch of the general field of quantum information science (QIS), is the quantum extension of Shannon's classical information theory. The past decade has seen an extraordinary amount of interest and effort in quantum information theory, spurred by quantum cryptography (which guarantees unconditionally secure communication) and the important role of error correction in overcoming decoherence in quantum computers (which are, in theory, capable of breaking RSA encryption). Intellectual Merit Hitherto quantum and classical information theory have been developed using an inefficient ``first principles'' approach: after the communication model has been defined, and a formula for the appropriate capacity region conjectured, ideas and techniques from related models are applied to the problem, with an ever-increasing degree of sophistication and complexity. This may be compared to computer programming directly in assembly language as opposed to using a high-level language like C++. The foundational aspect of this proposal focuses on the development a high-level, modular mathematical formalism for quantum and classical information theory, in which (i) all asymptotic coding theorems, as well certain general principles, are phrased as inequalities between information processing resources; (ii) a large class of coding theorems can be simply proved by manipulating these resource inequalities according to the rules of the resource calculus. Furthermore, such a framework provides structural insights into the logical dependencies among coding theorems. The practical aspect of this proposal regards translating these logical dependencies into coding strategies for the finite setting (such as new quantum error correction codes). The development and popularization of such a high-level framework has significant educational benefits as a compact organizing principle. The proposed program consists of four components: (I) the development of the resource calculus; (II) the classification of known resource inequalities into those which can (elementary) and cannot (composite) be made by combining others; (III) exploring new communication scenarios and establishing new coding theorems; (IV) applying the structural insights gained to practically relevant finite codes. Starting with the basic two party scenario, for each component complexity is increased in two independent directions (a) by adding more parties with varying roles (cooperative, adversarial, or passive) and (b) by imposing thermodynamically motivated constraints on local information processing. Broader Impact This proposal contains a further strong educational component, including: the incorporation of research ideas into the USC undergraduate curriculum; development of a graduate course in quantum communication theory; and the training of PhD students. The PI is currently writing a textbook entitled ``Principles of Quantum Information Theory'', with co-authors Patrick Hayden and Andreas Winter. The central role played by the resource calculus in this book will ensure that this project contributes meaningfully to educational and scientific activities of practical benefit to society. The PI will foster interdisciplinary collaborations and be active in contributing professionally to the broader QIS community.