Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sudden change of quantum discord for a system of two qubits

It is known that quantum discord might experience a sudden transition in its dynamics when calculated for certain Bell-diagonal states (BDS) that are in interaction with their surroundings. We examine this phenomenon, known as the sudden change of quantum discord, considering the case of two qubits independently interacting with dephasing reservoirs. We first demonstrate that, for a class of initial states which can be chosen arbitrarily close to BDS, the transition is in fact not sudden, although it might numerically appear so if not studied carefully. Then, we provide an extension of this discussion covering the X-shaped density matrices. Our findings suggest that the transition of quantum discord might be sudden only for an highly idealized zero-measure subset of states within the set of all possible initial conditions of two qubits. © 2013 American Physical Society.

Monogamy of entanglement of formation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Extracting Information from Qubit-Environment Correlations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Maximally genuine multipartite entangled mixed X-states of N-qubits

For every possible spectrum of 2(N)-dimensional density operators, we construct an N-qubit X-state of the same spectrum and maximal genuine multipartite (GM-) concurrence, hence characterizing a global unitary transformation that -constrained to output X-states-maximizes the GM-concurrence of an arbitrary input mixed state of N qubits. We also apply semidefinite programming methods to obtain N-qubit X-states with maximal GM-concurrence for a given purity and to provide an alternative proof of optimality of a recently proposed set of density matrices for the purpose, the so-called X-MEMS. Furthermore, we introduce a numerical strategy to tailor a quantum operation that converts between any two given density matrices using a relatively small number of Kraus operators. We apply our strategy to design short operator-sum representations for the transformation between any given N-qubit mixed state and a corresponding X-MEMS of the same purity.

Quantum state tomography and quantum logical operations in a three qubits NMR quadrupolar system

In this work, we present an implementation of quantum logic gates and algorithms in a three effective qubits system, represented by a (I = 7/2) NMR quadrupolar nuclei. To implement these protocols we have used the strong modulating pulses (SMP) and the various stages of each implementation were verified by quantum state tomography (QST). The results for the computational base states, Toffolli logic gates, and Deutsch-Jozsa and Grover algorithms are presented here. Also, we discuss the difficulties and advantages of implementing such protocols using the SMP technique in quadrupolar systems.

Bipartite graphs and quasipositive surfaces

We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links and discuss its potential relation with the adjacency problem for plane curve singularities.

The embryonic transcription factor stage specific activator protein contains a potent bipartite activation domain that interacts with several RNA polymerase II basal transcription factors.

Stage specific activator protein (SSAP) is a member of a newly discovered class of transcription factors that contain motifs more commonly found in RNA-binding proteins. Previously, we have shown that SSAP specifically binds to its recognition sequence in both the double strand and the single strand form and that this DNA-binding activity is localized to the N-terminal RNA recognition motif domain. Three copies of this recognition sequence constitute an enhancer element that is directly responsible for directing the transcriptional activation of the sea urchin late histone H1 gene at the midblastula stage of embryogenesis. Here we show that the remainder of the SSAP polypeptide constitutes an extremely potent bipartite transcription activation domain that can function in a variety of mammalian cell lines. This activity is as much as 3 to 5 times stronger than VP16 at activating transcription and requires a large stretch of amino acids that contain glutamine-glycine rich and serine-threonine-basic amino acid rich regions. We present evidence that SSAP's activation domain shares targets that are also necessary for activation by E1a and VP16. Finally, SSAP's activation domain is found to participate in specific interactions in vitro with the basal transcription factors TATA-binding protein, TFIIB, TFIIF74, and dTAF(II) 110.

Bipartite function of a small RNA hairpin in transcription antitermination in bacteriophage lambda.

Transcription of downstream genes in the early operons of phage lambda requires a promoter-proximal element known as nut. This site acts in cis in the form of RNA to assemble a transcription antitermination complex which is composed of lambda N protein and at least four host factors. The nut-site RNA contains a small stem-loop structure called boxB. Here, we show that boxB RNA binds to N protein with high affinity and specificity. While N binding is confined to the 5' subdomain of the stem-loop, specific N recognition relies on both an intact stem-loop structure and two critical nucleotides in the pentamer loop. Substitutions of these nucleotides affect both N binding and antitermination. Remarkably, substitutions of other loop nucleotides also diminish antitermination in vivo, yet they have no detectable effect on N binding in vitro. These 3' loop mutants fail to support antitermination in a minimal system with RNA polymerase (RNAP), N, and the host factor NusA. Furthermore, the ability of NusA to stimulate the formation of the RNAP-boxB-N complex is diminished with these mutants. Hence, we suggest that boxB RNA performs two critical functions in antitermination. First, boxB binds to N and secures it near RNAP to enhance their interaction, presumably by increasing the local concentration of N. Second, boxB cooperates with NusA, most likely to bring N and RNAP in close contact and transform RNAP to the termination-resistant state.

Structural basis for the specificity of bipartite nuclear localization sequence binding by importin-α

Importin-alpha is the nuclear import receptor that recognizes cargo proteins carrying conventional basic monopartite and bipartite nuclear localization sequences (NLSs) and facilitates their transport into the nucleus. Bipartite NLSs contain two clusters of basic residues, connected by linkers of variable lengths. To determine the structural basis of the recognition of diverse bipartite NLSs by mammalian importin-alpha, we co-crystallized a non-autoinhibited mouse receptor protein with peptides corresponding to the NLSs from human retinoblastoma protein and Xenopus laevis phosphoprotein N1N2, containing diverse sequences and lengths of the linker. We show that the basic clusters interact analogously in both NLSs, but the linker sequences adopt different conformations, whereas both make specific contacts with the receptor. The available data allow us to draw general conclusions about the specificity of NLS binding by importin-alpha and facilitate an improved definition of the consensus sequence of a conventional basic/bipartite NLS (KRX10-12KRRK) that can be used to identify novel nuclear proteins.

On the forced matching numbers of bipartite graphs

Let G be a graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M, such that S is contained in no other perfect matching of G. This notion has arisen in the study of finding resonance structures of a given molecule in chemistry. Similar concepts have been studied for block designs and graph colorings under the name defining set, and for Latin squares under the name critical set. There is some study of forcing sets of hexagonal systems in the context of chemistry, but only a few other classes of graphs have been considered. For the hypercubes Q(n), it turns out to be a very interesting notion which includes many challenging problems. In this paper we study the computational complexity of finding the forcing number of graphs, and we give some results on the possible values of forcing number for different matchings of the hypercube Q(n). Also we show an application to critical sets in back circulant Latin rectangles. (C) 2003 Elsevier B.V. All rights reserved.