— A generalized skew information is defined and a generalized uncertainty relation is established with the help of a trace inequality which was recently proven by J.I.Fujii. In addition, we prove the trace inequality conjectured by S.Luo and Z.Zhang. Finally we point out that Theorem 1 in S. is incorrect in general, by giving a simple counterexample .
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… (More)
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  are extended in terms of the parameter of the Tsallis relative operator entropy. Moreover the generalized Tsallis relative operator entropy is introduced and then several operator… (More)
A generalized skew correlation and a generalized skew information are defined and then a kind of the generalization of uncertainty relation is established by the help of the trace inequality which was recently proven by J.I.Fujii. In addition, we prove the trace inequality which is an extension of the conjecture addressed in . This manuscript is based on… (More)
We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixture. And we introduce a generalized Fisher information and then… (More)
Tsallis relative operator entropy was defined as a parametric extension of the relative operator entropy and the generalized Shannon inequalities were shown in the previous paper. After the review of some fundamental properties of the Tsallis relative operator entropy, some operator inequalities related to the Tsallis relative operator entropy are shown in… (More)