Quantum entropy and its applications to quantum communication and statistical physics (Q657471)

Summary: Quantum entropy is a fundamental concept for quantum information recently developed in various directions. We will review the mathematical aspects of quantum entropy (entropies) and discuss some applications to quantum communication, statistical physics. All topics taken here are somehow related to the quantum entropy that the present authors have been studied. Many other fields recently developed in quantum information theory, such as quantum algorithm, quantum teleportation, quantum cryptography, etc., are totally discussed in the book of \textit{I.V. Volovich} and the first author [Mathematical Foundation of Quantum Information and Computation (in preparation)].