On trace inequalities and their applications to noncommutative   communication theory
  Certain trace inequalities related to matrix logarithm are shown.   These results enable us to give a partial answer of the open problem conjectured by A.S.Holevo.   That is, concavity of the auxiliary function which appears in the random coding exponent as the lower bound of the quantum reliability function for general quantum states is proven in the case of $0\leq s\leq 1$. 
Kenjiro Yanagi, Shigeru Furuichi and Ken Kuriyama