The hypothesis testing problem of two quantum states is treated. We show a new inequality between the error of the first kind and the second kind, which complements the result of Hiai and Petz to establish the quantum version of Stein's lemma. The inequality is also used to show a bound on the first kind error when the power exponent for the second kind error exceeds the quantum relative entropy, and the bound yields the strong converse in the quantum hypothesis testing. Finally, we discuss the relation between the bound and the power exponent derived by Han and Kobayashi in the classical hypothesis testing. KeywordsQuantum hypothesis testing, Stein's lemma, strong converse, quantum relative entropy. IntroductionLet H be a Hilbert space which represents a physical system in interest. We suppose dim H < ∞ for mathematical simplicity. Let B(H) be the set of linear operators on H and putwhich is the set of density operators on H.We treat the problem of hypothesis testing a null hypothesis ρ ∈ S(H) versus an alternative hypothesis σ ∈ S(H). Here, we assume Im ρ ⊂ Im σ. To consider an asymptotic situation, suppose that either ρ ⊗n ∈ S(H ⊗n ) or σ ⊗n ∈ S(H ⊗n ) is given. The problem is to decide which hypothesis is true, and the decision is given by a two-valued quantum measurement {A n , 1 − A n } (A n ∈ B(H ⊗n ), 0 ≤ A n ≤ 1), where A n corresponds to the acceptance of ρ ⊗n and 1 − A n corresponds to the acceptance of σ ⊗n . We call A n ∈ B(H ⊗n ) (0 ≤ A n ≤ 1) a test in the sequel. * The authors are with the Graduate

We show that the new quantum extension of Rényi's α-relative entropies, introduced recently

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 except for the difficulty due to noncommutativity.

The carboxyl-terminal domain of colicin E5 was shown to inhibit protein synthesis of Escherichia coli. Its target, as revealed through in vivo and in vitro experiments, was not ribosomes as in the case of E3, but the transfer RNAs (tRNAs) for Tyr, His, Asn, and Asp, which contain a modified base, queuine, at the wobble position of each anticodon. The E5 carboxyl-terminal domain hydrolyzed these tRNAs just on the 3' side of this nucleotide. Tight correlation was observed between the toxicity of E5 and the cleavage of intracellular tRNAs of this group, implying that these tRNAs are the primary targets of colicin E5.

Colicin D has long been thought to stop protein synthesis in infected Escherichia coli cells by inactivating ribosomes, just like colicin E3. Here, we show that colicin D specifically cleaves tRNAs Arg including four isoaccepting molecules both in vivo and in vitro. The cleavage occurs in vitro between positions 38 and 39 in an anticodon loop with a 2 ,3 -cyclic phosphate end, and is inhibited by a specific immunity protein. Consistent with the cleavage of tRNAs Arg , the RNA fraction of colicin-treated cells significantly reduced the amino acid-accepting activity only for arginine. Furthermore, we generated a single mutation of histidine in the C-terminal possible catalytic domain, which caused the loss of the killing activity in vivo together with the tRNA Arg -cleaving activity both in vivo and in vitro. These findings show that colicin D directly cleaves cytoplasmic tRNAs Arg , which leads to impairment of protein synthesis and cell death. Recently, we found that colicin E5 stops protein synthesis by cleaving the anticodons of specific tRNAs for Tyr, His, Asn, and Asp. Despite these apparently similar actions on tRNAs and cells, colicins D and E5 not only exhibit no sequence homology but also have different molecular mechanisms as to both substrate recognition and catalytic reaction.C olicins are plasmid-encoded proteins that are toxic to Escherichia coli cells that do not have the same plasmid or a cognate Col plasmid (1-5). Most colicins are produced in response to SOS-inducing signals and are secreted into the medium. After binding to cell-surface receptors on sensitive cells, they are translocated across the membrane and then exert their final cytotoxic activities, which are attributable to their C-terminal domains. Two major modes of toxicity are well known; colicins A, B, E1, Ia, Ib, K, and N are ion-channel formers attacking the cytoplasmic membrane, and colicins E2 to E9 are nucleases. In the latter group, E2, E7, E8, and E9 are DNases, and E3 is a special kind of RNase that cleaves 16S rRNA within ribosomes.Colicins E4 to E6 quickly stop amino acid incorporation in treated cells (6), suggesting impairment of protein synthesis analogous in the established case of E3, which specifically cleaves 16S-RNA at the 49th bond from the 3Ј end leading to inactivation of ribosomes (7-9). This is also the case with colicin D, which Timmis and Hedges have characterized as to the physiological response of treated cells (10, 11), although the actual molecular basis of the cytotoxic effect of colicin D, as well as those of E4 to E6, remained to be elucidated. Colicins E4 and E6 proved to be E3-homologs and showed comparable activity toward ribosomes (ref. 12; GenBank accession number X63621; Y. Gunji, M. Ohno, T.O., H.M., and T.U., unpublished data), but colicin E5 exhibits no similarity to E3 in the C-terminal active domain. We recently showed that colicin E5 comprises a third category of nuclease-type colicins, which does not attack ribosomes but specific tRNAs (13). E5 is a novel RNase that cleaves the anticodons...