Abstract- (2005)]. Notably, we obtain an explicit construction of indistinguishable subspaces of dimension 7 (or 6) by considering a composite quantum system consisting of two qutrits (resp. three qubits), which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8.

In this study, we sequenced the first full-length insect transcriptome using the Erthesina fullo Thunberg based on the PacBio platform. We constructed the first quantitative transcription map of animal mitochondrial genomes and built a straightforward and concise methodology to investigate mitochondrial gene transcription, RNA processing, mRNA maturation and several other related topics. Most of the results were consistent with the previous studies, while to the best of our knowledge some findings were reported for the first time in this study. The new findings included the high levels of mitochondrial gene expression, the 3 0 polyadenylation and possible 5 0 m 7 G caps of rRNAs, the isoform diversity of 12S rRNA, the polycistronic transcripts and natural antisense transcripts of mitochondrial genes et al. These findings could challenge and enrich fundamental concepts of mitochondrial gene transcription and RNA processing, particularly of the rRNA primary (sequence) structure. The methodology constructed in this study can also be used to study gene expression or RNA processing of nuclear genomes.

We study the local distinguishability of general multi-qubit states and show that local projective measurements and classical communication are as powerful as the most general local measurements and classical communication. Remarkably, this indicates that the local distinguishability of multiqubit states can be decided efficiently. Another useful consequence is that a set of orthogonal n-qubit states is locally distinguishable only if the summation of their orthogonal Schmidt numbers is less than the total dimension 2 n . When n = 2 such a condition is also sufficient. Employing these results, we show that any orthonormal basis of a subspace spanned by arbitrary three-qubit orthogonal unextendible product bases (UPB) cannot be exactly distinguishable by local operations and classical communication. This not only reveals another intrinsic property of three-qubit orthogonal UPB, but also provides a class of locally indistinguishable subspaces with dimension 4. We also explicitly construct locally indistinguishable subspaces with dimensions 3 and 5, respectively. In particular, 3 is the minimal possible dimension of locally indistinguishable subspaces. Combining with the previous results, we conclude that any positive integer between 3 and 7 is the possible dimension of some three-qubit locally indistinguishable subspace.

Hemiptera is the largest order in Paraneoptera and the fifth largest in Insecta. Disputes about hemipteran phylogeny have concerned the monophyly of Auchenorrhyncha and relationships between the suborders Fulgoromorpha, Cicadomorpha, Coleorrhyncha and Heteroptera. In a phylogenomic study of Hemiptera, we add two new mitochondrial genomes of Peloridiidae (Coleorrhyncha) to those reported in GenBank, to complete the taxon sampling of all suborders. We used two types of data – amino acid sequences and nucleotides of various combinations between protein coding genes, tRNAs and rRNAs – to infer the phylogeny of Hemiptera. In total 27 taxa of Paraneoptera were sampled, 24 of them being hemipterans. Bayesian inference, maximum likelihood and maximum parsimony analyses were employed. The relationship of Cicadomorpha + Heteroptera is always stable in the results with different combinations between data types and phylogenetic methods, but our results challenge the monophyly of ‘Homoptera’ and Auchenorrhyncha. In evaluating the relative contribution of each gene, the phylograms generated by single genes CO1, ND1, ND2, ND4 and ND5, respectively, closely matched the tree yielded by the combined datasets. In light of the taxon‐sampling sensitivity of trees based on mitochondrial genomes, the results need to be tested with further data from nuclear genes.