Mathematical study of quantum information

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We developed new mathematical methods for quantum measurement theory, quantum set theory, quantum complexity theory, and quantum coding theory. We advanced the study of a universally valid reformulation of the uncertainty principle based on the Ozawa inequality. We experimentally observed the violation of Heisenberg's error-disturbance relation for the first time in the world and also confirmed the Ozawa inequality in the same experimental arrangement. We showed computational complexity, inevitable decoherence, and necessary physical resources for various models of quantum computation. Moreover, we developed a new coding to correcting those errors. Those results gave broad impacts on quantum information technology, related industries, and culture.