| 研究概要 |
1. Mathematical theory of convexity of operator or trace functionals. This line of research uses methods, including a number of operator inequalities, which we developed.
2. The study of quantum informational functionals. We discovered and proved a convexity property for the residual entropy of a quantum system, and for the entropy gain over one or multiple quantum channels. The discovery is based on recent advances in the theory of operator monotone functions and is reported in a paper published in the Journal of Statistical Physics and at the conference “Entropy in Quantum Mechanics: Recent advances”, June 25-26 2013. Paris, France. We also characterized the class of matrix entropies, which is a recent tool to establish concentration inequalities for random matrices.
3. The analysis of specific physical models to investigate the possible use of quantum information theory in statistical mechanics.
4. The theory of monotone and convex operator mappings. New results with applications in quantum physics have been obtained. We also characterized the non-commutative perspectives and initiated a study of so-called regular operator mappings with applications in matrix geometry.
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