In 2015 we obtained non-hermitian extensions of Heisenberg type and Schrödinger type uncertainty relations for generalized metric adjusted skew information or generalized metric adjusted correlation measure and gave the results of DouDu as corollaries. In this paper we define generalized quasimetric adjusted q skew information for different two generalized states and obtain corresponding uncertainty relation. The result is applied to the inequalities related to fidelity and trace distance for different two generalized states which were given by Audenaert et al; and Powers-St$\phi$rmer. Finally we state q uncertainty relations for generalized metric adjusted q skew information or generalized metric adjusted q correlation measure.

We give a trace inequality related to the uncertainty relation of generalized Wigner-Yanase-Dyson skew information which includes our result.

In this correspondence, we give several inherent properties of the capacity function of a Gaussian channel with and without feedback by using some operator inequalities and matrix analysis. We give a new proof method which is different from the method appearing in: K. Yanagi and H. W. Chen, "Operator inequality and its application to information theory," Taiwanese J. Math., vol. 4, no. 3, pp. 407-416, Sep. 2000. We obtain the following results: C/sub n,Z/(P) and C/sub n,FB,Z/(P) are both concave functions of P, C/sub n,Z/(P) is a convex function of the noise covariance matrix and C/sub n,FB,Z/(P) is a convex-like function of the noise covariance matrix. This new proof method is very elementary and the results shall help study the capacity of Gaussian channel. Finally, we state a conjecture concerning the convexity of C/sub n,FB,/spl middot//(P).

Reliability functions characterize the asymptotic behavior of the error probability for transmission of data on a channel. Holevo introduced the quantum channel, and gave an expression for a random-coding lower bound involving an auxiliary function. Holevo, Ogawa, and Nagaoka conjectured that this auxiliary function is concave. Here we give a proof of this conjecture.

This is an extension of results represented in ISIT2003. 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 for 0 /spl les/ s /spl les/ 1.

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.

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.

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.

Gives an upper bound on the finite block length capacity of the discrete-time nonstationary Gaussian channel with delayed feedback. With the aid of minimization of a quadratic form, it is proved that the L time-delayed feedback capacity C/sub nFB//sup L/(P) and the nonfeedback capacity C/sub n/(P) satisfy C/sub n/(P)/spl les/C/sub nFB//sup L/(P)/spl les/C/sub n/(P*) where P* is concretely given. The authors give a sufficient condition for C/sub nFB//sup L/(P) to be increased by L time-delayed feedback. Finally the authors also give a necessary and sufficient condition for C/sub nFB//sup 2/(P) of a class of Gaussian channel to be increased by 2 time-delayed feedback.>

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.>

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.>

The capacity is considered for Gaussian channels where the channel noise covariance is not the same as the constraint covariance. An upper bound is obtained; sharper results are obtained under additional assumptions.