A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces

Entanglement witnesses (EWs) constitute one of the most important entanglement detectors in quantum systems. Nevertheless, their complete characterization, in particular with respect to the notion of optimality, is still missing, even in the decomposable case. Here we show that for any qubit-qunit decomposable EW (DEW) W the three statements are equivalent: (i) the set of product vectors obeying \bra{e,f}W\ket{e,f}=0 spans the corresponding Hilbert space, (ii) W is optimal, (iii) W=Q^{\Gamma} with Q denoting a positive operator supported on a completely entangled subspace (CES) and \Gamma standing for the partial transposition. While, implications $(i)\Rightarrow(ii)$ and $(ii)\Rightarrow(iii)$ are known, here we prove that (iii) implies (i). This is a consequence of a more general fact saying that product vectors orthogonal to any CES in C^{2}\otimes C^{n} span after partial conjugation the whole space. On the other hand, already in the case of C^{3}\otimes C^{3} Hilbert space, there exist DEWs for which (iii) does not imply (i). Consequently, either (i) does not imply (ii), or (ii) does not imply (iii), and the above transparent characterization obeyed by qubit-qunit DEWs, does not hold in general.Comment: 13 pages, proof of lemma 4 corrected, theorem 3 removed, some parts improve

QUBIT4MATLAB V3.0: A program package for quantum information science and quantum optics for MATLAB

A program package for MATLAB is introduced that helps calculations in quantum information science and quantum optics. It has commands for the following operations: (i) Reordering the qudits of a quantum register, computing the reduced state of a quantum register. (ii) Defining important quantum states easily. (iii) Formatted input and output for quantum states and operators. (iv) Constructing operators acting on given qudits of a quantum register and constructing spin chain Hamiltonians. (v) Partial transposition, matrix realignment and other operations related to the detection of quantum entanglement. (vi) Generating random state vectors, random density matrices and random unitaries.Comment: 22 pages, no figures; small changes, published versio

Insights into the Transposable Mobilome of Paracoccus spp. (Alphaproteobacteria)

Several trap plasmids (enabling positive selection of transposition events) were used to identify a pool of functional transposable elements (TEs) residing in bacteria of the genus Paracoccus (Alphaproteobacteria). Complex analysis of 25 strains representing 20 species of this genus led to the capture and characterization of (i) 37 insertion sequences (ISs) representing 9 IS families (IS3, IS5, IS6, IS21, IS66, IS256, IS1182, IS1380 and IS1634), (ii) a composite transposon Tn6097 generated by two copies of the ISPfe2 (IS1634 family) containing two predicted genetic modules, involved in the arginine deiminase pathway and daunorubicin/doxorubicin resistance, (iii) 3 non-composite transposons of the Tn3 family, including Tn5393 carrying streptomycin resistance and (iv) a transposable genomic island TnPpa1 (45 kb). Some of the elements (e.g. Tn5393, Tn6097 and ISs of the IS903 group of the IS5 family) were shown to contain strong promoters able to drive transcription of genes placed downstream of the target site of transposition. Through the application of trap plasmid pCM132TC, containing a promoterless tetracycline resistance reporter gene, we identified five ways in which transposition can supply promoters to transcriptionally silent genes. Besides highlighting the diversity and specific features of several TEs, the analyses performed in this study have provided novel and interesting information on (i) the dynamics of the process of transposition (e.g. the unusually high frequency of transposition of TnPpa1) and (ii) structural changes in DNA mediated by transposition (e.g. the generation of large deletions in the recipient molecule upon transposition of ISPve1 of the IS21 family). We also demonstrated the great potential of TEs and transposition in the generation of diverse phenotypes as well as in the natural amplification and dissemination of genetic information (of adaptative value) by horizontal gene transfer, which is considered the driving force of bacterial evolution

The In Vitro Studies On Phage Mu Transposase

Bacteriophage Mu is one of the model systems to study DNA transposition. The availability of an in vitro soluble system greatly facilitates the dissection of the transposition mechanisms at the molecular levels. Several aspects of the in vitro mini-Mu DNA transposition have been dealt with in this thesis.;First, the flanking host DNA sequences on the strand cleavage step mediated by Mu transposase (Mu A protein) was investigated. We found that certain flanking host sequences could inhibit the strand cleavage step without affecting the earlier synapsis step. Furthermore, this cleavage defect could be overcome by the Mu B protein in the presence of ATP.;Second, the role of the 10 kDa C-terminal domain (domain III) of Mu transposase was studied. We showed that the cloned domain III was still functional in interacting with the Mu B protein in the absence of the 65 kDa N-terminal domain of Mu transposase. Deletion analysis revealed that the last 36 residues at the C-terminus of Mu transposase were involved in interacting with the Mu B protein. An intact C-terminus was required for efficient interactions between the Mu A and Mu B proteins.;Third, we mapped a novel non-specific DNA binding and nuclease activity in a 26 residue region (aa575-600) at N-terminus of domain III of Mu transposase. We showed that this region was required in both early synapsis step and the subsequent strand cleavage step. We argue that this 26 residue region might contact the Mu-host junctions in the transpososomes. Complementation studies further suggest that the active sites for the strand cleavage activity of Mu transposase are made up of amino acids in this 26 residue region of domain III on one transposase monomer and the conserved acidic residues (D, D35E) of domain II on a separate transposase monomer

The spectra of finite 3-transposition groups

We calculate the spectrum of the diagram for each finite $3$-transposition group. Such graphs with a given minimal eigenvalue have occurred in the context of compact Griess subalgebras of vertex operator algebras

A comparative study of Tam3 and Ac transposition in transgenic tobacco and petunia plants

Transposition of the Anthirrinum majus Tam3 element and the Zea mays Ac element has been monitored in petunia and tobacco plants. Plant vectors were constructed with the transposable elements cloned into the leader sequence of a marker gene. Agrobacterium tumefaciens-mediated leaf disc transformation was used to introduce the transposable element constructs into plant cells. In transgenic plants, excision of the transposable element restores gene expression and results in a clearly distinguishable phenotype. Based on restored expression of the hygromycin phosphotransferase II (HPTII) gene, we established that Tam3 excises in 30% of the transformed petunia plants and in 60% of the transformed tobacco plants. Ac excises from the HPTII gene with comparable frequencies (30%) in both plant species. When the β-glucuronidase (GUS) gene was used to detect transposition of Tam3, a significantly lower excision frequency (13%) was found in both plant species. It could be shown that deletion of parts of the transposable elements Tam3 and Ac, removing either one of the terminal inverted repeats (TIR) or part of the presumptive transposase coding region, abolished the excision from the marker genes. This demonstrates that excision of the transposable element Tam3 in heterologous plant species, as documented for the autonomous element Ac, also depends on both properties. Southern blot hybridization shows the expected excision pattern and the reintegration of Tam3 and Ac elements into the genome of tobacco plants.

Integrable mappings and polynomial growth

We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds of transformations on $q \times q$ matrices: the inversion of the $q \times q$ matrix and an (involutive) permutation of the entries of the matrix. We concentrate on the case where these permutations are elementary transpositions of two entries. In this case the birational transformations fall into six different classes. For each class we analyze the factorization properties of the iteration of these transformations. These factorization properties enable to define some canonical homogeneous polynomials associated with these factorization properties. Some mappings yield a polynomial growth of the complexity of the iterations. For three classes the successive iterates, for $q=4$, actually lie on elliptic curves. This analysis also provides examples of integrable mappings in arbitrary dimension, even infinite. Moreover, for two classes, the homogeneous polynomials are shown to satisfy non trivial non-linear recurrences. The relations between factorizations of the iterations, the existence of recurrences on one or several variables, as well as the integrability of the mappings are analyzed.Comment: 45 page

A study of separability criteria for mixed three-qubit states

We study the noisy GHZ-W mixture. We demonstrate some necessary but not sufficient criteria for different classes of separability of these states. It turns out that the partial transposition criterion of Peres and the criteria of G\"uhne and Seevinck dealing with matrix elements are the strongest ones for different separability classes of this 2 parameter state. As a new result we determine a set of entangled states of positive partial transpose.Comment: 18 pages, 10 figures, PRA styl