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Generalized Shannon inequalities based on Tsallis relative operator entropy
Kenjiro Yanagi, Ken Kuriyama, Shigeru Furuichi
Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta \cite{Fu:par}…
Tsallis relative operator entropy in mathematical physics
S. Furuichi, K. Yanagi, K. Kuriyama
Tsallis relative operator entropy is defined as a parametric extension of the relative operator entropy. Some properties of the Tsallis relative operator entropy are investigated.…
Fundamental properties of Tsallis relative entropy
S. Furuichi, K. Yanagi, K. Kuriyama
Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace…
On trace inequalities and their applications to noncommutative communication theory
Kenjiro Yanagi, Shigeru Furuichi, Ken Kuriyama
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…