Laboratory of Mathematical Structures III

Prof. Masanao Ozawa

Japanese version is here.

This laboratory is concerned with the research and education of quantum information. Every information transmission or information processing is subjected to laws of physics. Although conventional information systems can be well described by classical physics, Moor's law, an empirical law on the speed of evolution of information technology, predicts the need for information systems based on quantum physics realized within 20 years.

To construct a comprehensive theory of quantum information, the laboratory is undertaking the following research projects.

1. Quantum computing theory.
This includes quantum complexity theory and quantum algorithms from a computer science approach, and quantum theory of logic operations and quantum error-correcting codes from a quantum mechanics approach.

2. Quantum information theory.
This includes quantum entropy, quantum channel capacity, entanglement, quantum estimation, quantum teleportations.

3. Quantum measurement theory.
This is a new theory emerging from quantum theory of open systems by considering the information output from dynamical processes of open systems. This is a key theory to obtain a correct description of the uncertainty principle and to achieve unifying quantum mechanics and information theory.

In advancing the above projects, notions and methods are involved relative to functional analysis, noncommutative probability theory, information theory, nonstandard analysis, computational complexity, and cryptography in mathematics, and also relative to quantum mechanics, quantum optics, and statistical mechanics, from which we expect to produce new mathematics, physics, and information sciences.