Strong Converse to the Quantum Channel Coding Theorem

A lower bound on the probability of decoding error of quantum communication channel is presented. The strong converse to the quantum channel coding theorem is shown immediately from the lower bound. It is the same as Arimoto's method exept for the difficulty due to non-commutativity.Comment: LaTeX, 11 pages, submitted to IEEE Trans. Inform. Theor

Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions

There are different inequivalent ways to define the R\'enyi capacity of a channel for a fixed input distribution $P$. In a 1995 paper Csisz\'ar has shown that for classical discrete memoryless channels there is a distinguished such quantity that has an operational interpretation as a generalized cutoff rate for constant composition channel coding. We show that the analogous notion of R\'enyi capacity, defined in terms of the sandwiched quantum R\'enyi divergences, has the same operational interpretation in the strong converse problem of classical-quantum channel coding. Denoting the constant composition strong converse exponent for a memoryless classical-quantum channel $W$ with composition $P$ and rate $R$ as $sc(W,R,P)$, our main result is that $$sc(W,R,P)=\sup_{\alpha>1}\frac{\alpha-1}{\alpha}\left[R-\chi_{\alpha}^*(W,P)\right],$$ where $\chi_{\alpha}^*(W,P)$ is the $P$-weighted sandwiched R\'enyi divergence radius of the image of the channel.Comment: 46 pages. V7: Added the strong converse exponent with cost constrain

Antioxidant Activity of Intramolecularly Hydrogen Bonded 2-Aminophenol

The antioxidant activities of five classes of 2-aminophenol (model compound) and 2-aminophenols with substituent at the phenyl ring were studied in the oxidation of tetralin induced by an azo-initiator at 61℃. 2-Aminophenols with electron-donating groups at the 4-position exhibited higher antioxidant activity than that of the model compound. However, introduction of the methoxy group at the 4-position reduced the antioxidant activity by 8 % that of the model compound. 2-Aminophenols with electron-donating groups at the 5-position have little effect on the antioxidant activity. 2-Aminophenols with electron-donating groups at both the 4- and 6-positions showed remarkable antioxidant activity. These results were discussed in terms of the hydrogen bonding effect and bond dissociation energies of the O-H and NH-H bonds