Kenjiro Yanagi

Fundamental properties of Tsallis relative entropy

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 inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hiai and Petz. The monotonicity of the quantum Tsallis relative entropy for the trace preserving completely positive linear map is also shown without the assumption that the density operators are invertible. The generalized Tsallis relative entropy is defined and its subadditivity is shown by its joint convexity. Moreover, the generalized Peierls–Bogoliubov inequality is also proven.

A generalized skew information and uncertainty relation

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 Fujii. In addition, we prove the trace inequality conjectured by Luo and Zhang. Finally, we point out that Theorem 1 in S. Luo and Q. Zhang, IEEE Trans. Inf. Theory, vol. 50, pp. 1778-1782, no. 8, Aug. 2004 is incorrect in general, by giving a simple counter-example.

Capacity of discrete time Gaussian channel with and without feedback, II

The problem considered in this paper is whether the capacity of a discrete time Gaussian channel is increased by feedback or not. It is well known that the capacity of a white Gaussian channel under the average power constraint is not changed by feedback. We give some conditions under which the capacity of a discrete time Gaussian channel is increased by feedback. It is also shown that there exists a non-white Gaussian channel whose capacity is not increased by feedback.

An upper bound to the capacity of discrete time Gaussian channel with feedback. II

We give an upper bound on the finite block length capacity of a discrete time nonstationary Gaussian channel with feedback. With the aid of minimization of a quadratic form, it is proved that the feedback capacity C/sub n,FB/(P) and the nonfeedback capacity C/sub n/(P) satisfy C/sub n/(P)/spl les/C/sub n,FB/(P)/spl les/C/sub n/(P/sup */) where P/sup */ is concretely given. >

Refinements of the half-bit and factor-of-two bounds for capacity in Gaussian channel with feedback

We consider the upper bounds of the finite blocklength capacity C/sub n,FB/(P) of the discrete time Gaussian channel with feedback. We also let C/sub n/(p) be the nonfeedback capacity. We prove the relations C/sub n/(P)/spl les/C/sub n,FB/(P)/spl les/C/sub n/(/spl alpha/P)+ 1/2 ln(1+1//spl alpha/) and C/sub n/(P)/spl les/C/sub n,FB/(P)/spl les/(1+1//spl alpha/)C/sub n/(/spl alpha/P) for any P>0 and any /spl alpha/>0, which induce the half-bit and factor-of-two bounds given by Cover and Pombra (1989) in the special case of /spl alpha/=1.

Schrödinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure

Abstract In this paper, we give Schrodinger-type uncertainty relation using the Wigner–Yanase–Dyson skew information. In addition, we give Schrodinger-type uncertainty relation by use of a two-parameter extended correlation measure. We finally show a further generalization of Schrodinger-type uncertainty relation by use of the metric adjusted correlation measure. These results generalize our previous result in [Phys. Rev. A 82 (2010) 034101].

Necessary and sufficient condition for capacity of the discrete time Gaussian channel to be increased by feedback

The problem of whether the capacity of a discrete-time Gaussian channel is increased by feedback or not is considered. It is well known that the capacity of a white Gaussian channel under an average power constraint is not changed by feedback. The necessary condition under which the capacity of a nonwhite Gaussian channel with blockwise white noise is increased by feedback is given. >

Upper bounds on the capacity of discrete-time blockwise white Gaussian channels with feedback

Although it is well known that feedback does not increase the capacity of an additive white Gaussian channel, Yanagi (1992) gave the necessary and sufficient condition under which the capacity C/sub n,FB/(P) of a discrete time nonwhite Gaussian channel is increased by feedback. In this correspondence we show that the capacity C/sub n,FB/(P) of the Gaussian channel with feedback is a concave function of P, and give two types of inequalities: both 1//spl alpha/ C/sub n,FB/(/spl alpha/P) and C/sub n,FB/(/spl alpha/P)+ 1/2 ln 1//spl alpha/ are decreasing functions of /spl alpha/>0. As their application we can obtain two upper bounds on the capacity of the discrete-time blockwise white Gaussian channel with feedback. The results are quite useful when power constraint P is relatively not large.

Uncertainty relations for generalized metric adjusted skew information and generalized metric adjusted correlation measure

AbstractIn this paper, we give a Heisenberg-type or a Schrödinger-type uncertainty relation for generalized metric adjusted skew information or generalized metric adjusted correlation measure. These results generalize the previous result of Furuichi and Yanagi (J. Math. Anal. Appl. 388:1147-1156, 2012).AMSPrimary: 15A45, 47A63; secondary: 94A17

Wigner-Yanase-Dyson skew information and uncertainty relation

We give a trace inequality related to the uncertainty relation of Wigner-Yanase-Dyson skew information. This inequality corresponds to a generalization of the uncertainty relation derived by S.Luo [8] for the quantum uncertainty quantity excluding the classical mixture. Finally we show a counter-example of the uncertainty relation related to Wigner-Yanase-Dyson skew information given in [6] recently.