CIF: Small: Learning Quantum Information Measures

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Quantum information processing systems are becoming practical with the expectation that these systems will soon be commercialized within a decade, and will be a part of our everyday life. However, our understanding of the amount of information that can be gleaned from a quantum system is still very rudimentary. For example, the complexity of the basic question of learning a quantum state (called tomography) was only resolved in the past few years, whereas its classical analogue of distribution estimation is now textbook material in any introductory statistics course. Research under this award will be dedicated to the study of the problem of estimating fundamental information measures, as well as introduce new information measures for quantum systems. The project will establish the fundamental limits of the information processing capabilities of quantum information systems, as well as design novel algorithms that can match these limits. The project outcomes can enable the development of efficient quantum computer and communication systems.The award will develop a deeper understanding of a quantum system as a statistical mechanism, and integrate ideas from various disciplines such as representation theory, information theory, statistics, and computer science. A novel variation of the statistical principle of maximum likelihood estimation as a general methodology for quantum property estimation will be proposed and developed. The project will also study the extension of representation theory results of Schur-Weyl duality to higher dimensions to obtain optimal quantum measurement schemes for properties of multiple quantum systems. The work includes proposing measurement schemes that are more realistic than the theoretically-optimal ones considered in the literature that in practice are too complex to be implemented with existing technology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.