Hitting time expressions for quantum channels: beyond the irreducible case and applications to unitary walks

In this work we make use of generalized inverses associated with quantum channels acting on finite-dimensional Hilbert spaces, so that one may calculate the mean hitting time for a particle to reach a chosen goal subspace. The questions studied in this work are motivated by recent results on quantum dynamics on graphs, most particularly quantum Markov chains. We focus on describing how generalized inverses and hitting times can be obtained, with the main novelties of this work with respect to previous ones being that a) we are able to weaken the notion of irreducibility, so that reducible examples can be considered as well, and b) one may consider arbitrary arrival subspaces for general positive, trace preserving maps. Natural examples of reducible maps are given by unitary quantum walks. We also take the opportunity to explain how a more specific inverse, namely the group inverse, appears in our context, in connection with matrix algebraic constructions which may be of independent interest

A dynamical point of view of Quantum Information: Wigner measures

We analyze a known version of the discrete Wigner function and some connections with Quantum Iterated Funcion Systems. This paper is a follow up of "A dynamical point of view of Quantum Information: entropy and pressure" by the same authors

A dynamical point of view of Quantum Information: entropy and pressure

Quantum Information is a new area of research which has been growing rapidly since last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more "dynamical point of view" of this theory. We want to consider the concepts of entropy and pressure for "stationary systems" acting on density matrices which generalize the usual ones in Ergodic Theory (in the sense of the Thermodynamic Formalism of R. Bowen, Y. Sinai and D. Ruelle). We consider the operator $\mathcal{L}$ acting on density matrices $\rho\in \mathcal{M}_N$ over a finite $N$-dimensional complex Hilbert space $\mathcal{L}(\rho):=\sum_{i=1}^k tr(W_i\rho W_i^*)V_i\rho V_i^*,$ where $W_i$ and $V_i$, $i=1,2,...k$ are operators in this Hilbert space. $\mathcal{L}$ is not a linear operator. In some sense this operator is a version of an Iterated Function System (IFS). Namely, the $V_i\,(.)\,V_i^*=:F_i(.)$, $i=1,2,...,k$, play the role of the inverse branches (acting on the configuration space of density matrices $\rho$) and the $W_i$ play the role of the weights one can consider on the IFS. We suppose that for all $\rho$ we have that $\sum_{i=1}^k tr(W_i\rho W_i^*)=1$. A family $W:=\{W_i\}_{i=1,..., k}$ determines a Quantum Iterated Function System (QIFS) $\mathcal{F}_{W}$, $\mathcal{F}_W=\{\mathcal{M}_N,F_i,W_i\}_{i=1,..., k}.

A Thermodynamic Formalism for density matrices in Quantum Information

We consider new concepts of entropy and pressure for stationary systems acting on density matrices which generalize the usual ones in Ergodic Theory. Part of our work is to justify why the definitions and results we describe here are natural generalizations of the classical concepts of Thermodynamic Formalism (in the sense of R. Bowen, Y. Sinai and D. Ruelle). It is well-known that the concept of density operator should replace the concept of measure for the cases in which we consider a quantum formalism. We consider the operator $\Lambda$ acting on the space of density matrices $\mathcal{M}_N$ over a finite $N$-dimensional complex Hilbert space $$\Lambda(\rho):=\sum_{i=1}^k tr(W_i\rho W_i^*)\frac{V_i\rho V_i^*}{tr(V_i\rho V_i^*)},$$ where $W_i$ and $V_i$, $i=1,2,..., k$ are linear operators in this Hilbert space. In some sense this operator is a version of an Iterated Function System (IFS). Namely, the $V_i\,(.)\,V_i^*=:F_i(.)$, $i=1,2,...,k$, play the role of the inverse branches (i.e., the dynamics on the configuration space of density matrices) and the $W_i$ play the role of the weights one can consider on the IFS. In this way a family $W:=\{W_i\}_{i=1,..., k}$ determines a Quantum Iterated Function System (QIFS). We also present some estimates related to the Holevo bound

Quantum Stochastic Processes, Quantum Iterated Function Systems and Entropy

We describe some basic results for Quantum Stochastic Processes and present some new results about a certain class of processes which are associated to Quantum Iterated Function Systems (QIFS). We discuss questions related to the Markov property and we present a de nition of entropy which is induced by a QIFS. This definition is a natural generalization of the Shannon-Kolmogorov entropy from Ergodic Theory

Overexpression of Arabidopsis FLOWERING LOCUS T (FT) gene improves floral development in cassava (Manihot esculenta, Crantz)

Cassava is a tropical storage-root crop that serves as a worldwide source of staple food for over 800 million people. Flowering is one of the most important breeding challenges in cassava because in most lines flowering is late and non-synchronized, and flower production is sparse. The FLOWERING LOCUS T (FT) gene is pivotal for floral induction in all examined angiosperms. The objective of the current work was to determine the potential roles of the FT signaling system in cassava. The Arabidopsis thaliana FT gene (atFT) was transformed into the cassava cultivar 60444 through Agrobacterium-mediated transformation and was found to be overexpressed constitutively. FT overexpression hastened flower initiation and associated fork-type branching, indicating that cassava has the necessary signaling factors to interact with and respond to the atFT gene product. In addition, overexpression stimulated lateral branching, increased the prolificacy of flower production and extended the longevity of flower development. While FT homologs in some plant species stimulate development of vegetative storage organs, atFT inhibited storage-root development and decreased root harvest index in cassava. These findings collectively contribute to our understanding of flower development in cassava and have the potential for applications in breeding

Evolutionary view of acyl-CoA diacylglycerol acyltransferase (DGAT), a key enzyme in neutral lipid biosynthesis

<p>Abstract</p> <p>Background</p> <p>Triacylglycerides (TAGs) are a class of neutral lipids that represent the most important storage form of energy for eukaryotic cells. DGAT (acyl-CoA: diacylglycerol acyltransferase; EC 2.3.1.20) is a transmembrane enzyme that acts in the final and committed step of TAG synthesis, and it has been proposed to be the rate-limiting enzyme in plant storage lipid accumulation. In fact, two different enzymes identified in several eukaryotic species, DGAT1 and DGAT2, are the main enzymes responsible for TAG synthesis. These enzymes do not share high DNA or protein sequence similarities, and it has been suggested that they play non-redundant roles in different tissues and in some species in TAG synthesis. Despite a number of previous studies on the DGAT1 and DGAT2 genes, which have emphasized their importance as potential obesity treatment targets to increase triacylglycerol accumulation, little is known about their evolutionary timeline in eukaryotes. The goal of this study was to examine the evolutionary relationship of the DGAT1 and DGAT2 genes across eukaryotic organisms in order to infer their origin.</p> <p>Results</p> <p>We have conducted a broad survey of fully sequenced genomes, including representatives of Amoebozoa, yeasts, fungi, algae, musses, plants, vertebrate and invertebrate species, for the presence of DGAT1 and DGAT2 gene homologs. We found that the DGAT1 and DGAT2 genes are nearly ubiquitous in eukaryotes and are readily identifiable in all the major eukaryotic groups and genomes examined. Phylogenetic analyses of the DGAT1 and DGAT2 amino acid sequences revealed evolutionary partitioning of the DGAT protein family into two major DGAT1 and DGAT2 clades. Protein secondary structure and hydrophobic-transmembrane analysis also showed differences between these enzymes. The analysis also revealed that the MGAT2 and AWAT genes may have arisen from DGAT2 duplication events.</p> <p>Conclusions</p> <p>In this study, we identified several DGAT1 and DGAT2 homologs in eukaryote taxa. Overall, the data show that DGAT1 and DGAT2 are present in most eukaryotic organisms and belong to two different gene families. The phylogenetic and evolutionary analyses revealed that DGAT1 and DGAT2 evolved separately, with functional convergence, despite their wide molecular and structural divergence.</p

An integrated bioinformatics analysis reveals divergent evolutionary pattern of oil biosynthesis in high- and low-oil plants

Seed oils provide a renewable source of food, biofuel and industrial raw materials that is important for humans. Although many genes and pathways for acyl-lipid metabolism have been identified, little is known about whether there is a specific mechanism for high-oil content in high-oil plants. Based on the distinct differences in seed oil content between four high-oil dicots (20~50%) and three low-oil grasses (<3%), comparative genome, transcriptome and differential expression analyses were used to investigate this mechanism. Among 4,051 dicot-specific soybean genes identified from 252,443 genes in the seven species, 54 genes were shown to directly participate in acyl-lipid metabolism, and 93 genes were found to be associated with acyl-lipid metabolism. Among the 93 dicot-specific genes, 42 and 27 genes, including CBM20-like SBDs and GPT2, participate in carbohydrate degradation and transport, respectively. 40 genes highly up-regulated during seed oil rapid accumulation period are mainly involved in initial fatty acid synthesis, triacylglyceride assembly and oil-body formation, for example, ACCase, PP, DGAT1, PDAT1, OLEs and STEROs, which were also found to be differentially expressed between high- and low-oil soybean accessions. Phylogenetic analysis revealed distinct differences of oleosin in patterns of gene duplication and loss between high-oil dicots and low-oil grasses. In addition, seed-specific GmGRF5, ABI5 and GmTZF4 were predicted to be candidate regulators in seed oil accumulation. This study facilitates future research on lipid biosynthesis and potential genetic improvement of seed oil content