Error probability analysis in quantum tomography: a tool for evaluating experiments

We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can decrease at most exponentially in the number of trials, derive the explicit rate that bounds this decrease, and show that a maximum likelihood estimator achieves this bound. We also show that the statistical notion of identifiability coincides with the tomographic notion of informational completeness. Our result implies that two quantum tomographic apparatuses that have the same risk function, (e.g. variance), can have different error probability, and we give an example in one qubit state tomography. Thus by combining these two approaches we can evaluate, in a reconstruction independent way, the performance of such experiments more discerningly.Comment: 14pages, 2 figures (an analysis of an example is added, and the proof of Lemma 2 is corrected

Mutation of the N-terminal proline 9 of BLMA from Streptomyces verticillus abolishes the binding affinity for bleomycin

AbstractA gene, blmA, from bleomycin (Bm)-producing Streptomyces verticillus, encodes a Bm-binding protein, designated BLMA. The expression of BLMA conferred resistance to Bm in the Escherichia coli host, whereas a mutant protein, designated Pro-9/Leu, with the N-terminal proline 9 residue in BLMA replaced by leucine, did not. We created a fusion protein between the maltose-binding protein (MBP) and a mutant protein Pro-9/Leu/Leu with Met-94 in Pro-9/Leu replaced by leucine. Pro-9/Leu/Leu from the fusion protein, obtained by digestion with CNBr digestion, did not inhibit DNA-cleaving and antibacterial activities of Bm. Native-polyacrylamide gel electrophoresis (PAGE) and gel filtration column chromatographic analysis showed that the molecular size of Pro-9/Leu/Leu is roughly half of that of BLMA, suggesting that the mutant protein cannot form dimeric structure. Furthermore, Far-UV circular dichroism (CD) spectrum of Pro-9/Leu/Leu was quite different from that of BLMA and similar to the spectra obtained from unordered proteins [Venyaminov, S.Y. and Vassilenko, K.S. (1994) Anal. Biochem. 222, 176–184], suggesting that the secondary structure of Pro-9/Leu/Leu is disrupted. These results indicate that the mutation abolishes not only dimer formation but also the secondary structure of BLMA, which results in the loss of its function as a Bm-resistance determinant

Effect of nonnegativity on estimation errors in one-qubit state tomography with finite data

We analyze the behavior of estimation errors evaluated by two loss functions, the Hilbert-Schmidt distance and infidelity, in one-qubit state tomography with finite data. We show numerically that there can be a large gap between the estimation errors and those predicted by an asymptotic analysis. The origin of this discrepancy is the existence of the boundary in the state space imposed by the requirement that density matrices be nonnegative (positive semidefinite). We derive an explicit form of a function reproducing the behavior of the estimation errors with high accuracy by introducing two approximations: a Gaussian approximation of the multinomial distributions of outcomes, and linearizing the boundary. This function gives us an intuition for the behavior of the expected losses for finite data sets. We show that this function can be used to determine the amount of data necessary for the estimation to be treated reliably with the asymptotic theory. We give an explicit expression for this amount, which exhibits strong sensitivity to the true quantum state as well as the choice of measurement.Comment: 9 pages, 4 figures, One figure (FIG. 1) is added to the previous version, and some typos are correcte

Cloning and Characterization of a Streptomyces Single Module Type Non-ribosomal Peptide Synthetase Catalyzing a Blue Pigment Synthesis

In the present study, we cloned a gene, designated bpsA, which encodes a single module type non-ribosomal peptide synthetase (NRPS) from a d-cycloserine (DCS)-producing Streptomyces lavendulae ATCC11924. A putative oxidation domain is significantly integrated into the adenylation domain of the NRPS, and the condensation domain is absent from the module. When S. lividans was transformed with a plasmid carrying bpsA, the transformed cells produced a blue pigment, suggesting that bpsA is responsible for the blue pigment synthesis. However, to produce the blue pigment in Escherichia coli, the existence of the 4′-phosphopantetheinyl transferase (PPTase) gene from Streptomyces was necessary, in addition to bpsA. The chemical structure of the pigment was determined as 5,5′-diamino-4,4′-dihydroxy-3,3′-diazadiphenoquinone-(2,2′), called indigoidine. The bpsA gene product, designated BPSA, was overproduced in an E. coli host-vector system and purified to homogeneity, demonstrating that the recombinant enzyme prefers l-Gln as a substrate. The in vitro experiment using l-Gln also showed that the blue pigment was formed by the purified BPSA only when the enzyme was phosphopantetheinylated by adding a Streptomyces PPTase purified from E. coli cells. Each site-directed mutagenesis experiment of Lys598, Tyr601, Ser603, and Tyr608, which are seen in the oxidation domain of BPSA, suggests that these residues are essential for the binding of FMN to the protein and the synthesis of the blue pigment