arXiv subjects

Shigeru Furuichi

Publications and source records attributed to Shigeru Furuichi.

79 records · Page 5Linked to original sources

arXiv2005

On uniqueness theorems for Tsallis entropy and Tsallis relative entropy

The uniqueness theorem for Tsallis entropy was presented in {\it H.Suyari, IEEE Trans. Inform. Theory, Vol.50, pp.1783-1787 (2004)} by introducing the generalized Shannon-Khinchin's axiom. In the present paper, this result is generalized and simplified as follows: {\it Generalization}: The uniqueness theorem for Tsallis relative entropy is shown by means of the generalized Hobson's axiom. {\it Simplification}: The uniqueness theorem for Tsallis entropy is shown by means of the generalized Faddeev's axiom.

cond-mat.stat-mech↗

arXiv2005

Generalized Shannon inequalities based on Tsallis relative operator entropy

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} 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 inequalities are derived.

math.FA↗

arXiv2005

A note on operator inequalities of Tsallis relative operator entropy

Tsallis relative operator entropy was defined as a parametric extension of relative operator entropy and the generalized Shannon inequalities were shown in the previous paper. After the review of some fundamental properties of Tsallis relative operator entropy, some operator inequalities related to Tsallis relative operator entropy are shown in the present paper. Our inequalities give the upper and lower bounds of Tsallis relative operator entropy. The operator equality on Tsallis relative operator entropy is also shown by considering the tensor product. This relation generalizes the pseudoadditivity for Tsallis entropy. As a corollary of our operator equality derived from the tensor product manipulation, we show several operator inequalities including the superadditivity and the subadditivity for Tsallis relative operator entropy. Our results are generalizations of the superadditivity and the subadditivity for Tsallis entropy.

math.FA↗

arXiv2005

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 $0\leq s\leq 1$.

quant-ph↗

arXiv2005

An elementary formula for entanglement entropies of fermionic systems

An elementary formula for the von Neumann and Renyi entropies describing quantum correlations in two-fermionic systems having four single particle states is presented. An interesting geometric structure of fermionic entanglement is revealed. A connection with the generalized Pauli principle is established.

quant-ph↗

arXiv2001

Entanglement in squeezed two-level atom

In the previous paper, we adopted the method using quantum mutual entropy to measure the degree of entanglement in the time development of the Jaynes-Cummings model. In this paper, we formulate the entanglement in the time development of the Jaynes-Cummings model with squeezed states, and then show that the entanglement can be controlled by means of squeezing.

quant-ph↗

arXiv1998

Quantum mutual entropy for Jaynes-Cummings model

The dynamics of an atom on the Jaynes-Cummings model has been studied by an atomic inversion, von Neumann entropy and so on. In this letter, we will treat the Jaynes-Cummings model as a problem in non-equilibrium statistical mechanics and apply quantum mutual entropy to study the irreversible dynamics of a state for the atom on this model.

quant-ph↗