Measurement of qubits

We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (qubits). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices that are always non-negative definite). In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.

Predictions of quantum mechanics and stochastic electrodynamics in travelling wave second harmonic generation

We show that stochastic electrodynamics and quantum mechanics give quantitatively different predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semiclassical results are different in the regions where the system performs best in relation to the QND criteria, and that they significantly overestimate the performance in these regions. (C) 2001 Published by Elsevier Science B.V.

A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element, Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates, (C) 2001 Elsevier Science Ltd, All rights reserved.

Post-antibiotic growth suppression of linezolid against Gram-positive bacteria

The in vitro post-antibiotic effects (PAEs) of eight different concentrations of linezolid against Gram-positive cocci were investigated and the results analysed using the sigmoid E-max model for mathematically modelling the PAE. Mean maximal linezolid PAEs against strains of Staphylococcus aureus, Staphylococcus epidermidis, Enterococcus faecalis, Enterococcus faecium and Streptococcus pneumoniae were 2.2, 1.8, 2.8, 2.0 and 3.0 h, respectively. Resistance to methicillin (for the staphylococci), vancomycin (for the enterococci) and penicillin (for the pneumococci) had no effect on the duration of the PAE. Results of PAE testing support twice-daily dosing of linezolid in humans.

The effectiveness of splinting as perceived by the parents of children with Juvenile Ideopathic Arthritis

Juvenile idiopathic arthritis (JIA) is an important disease of childhood with farreaching effects on the child and family. Splinting is a major treatment modality used by occupational therapists for children with JIA. Parents play a central role in whether, when and how splints are used with their children on a daily basis. This paper describes a qualitative research project, which was undertaken to evaluate an occupational therapy service for children with JIA whose treatment had involved splinting. Using semi-structured interviews, the study investigated five mothers' perceptions of the effectiveness of splinting for their children. The interviews revealed five major points. First, the informants generally believed the splinting to be effective. Secondly, the children involved generally resisted wearing splints because they were physically uncomfortable and made them feel different to other children. Thirdly, the mothers used a variety of strategies to ensure that their children wore the splints. Fourthly, the perception of having a positive and supportive relationship with the therapist enhanced the mothers' ability to adhere to splinting. Lastly, the mothers' grief at having a child with JIA influenced their ability to understand and attend to information about specific interventions such as splinting. Practical responses to these findings are outlined.

Positive-P and Wigner representations for quantum-optical systems with nonorthogonal modes

We generalize the basic concepts of the positive-P and Wigner representations to unstable quantum-optical systems that are based on nonorthogonal quasimodes. This lays the foundation for a quantum description of such systems, such as, for example an unstable cavity laser. We compare both representations by calculating the tunneling times for an unstable resonator optical parametric oscillator.

Positive genetic correlation between female preference and offspring fitness

In many species, females display preferences for extreme male signal traits, but it has not been determined if such preferences evolve as a consequence of females gaining genetic benefits from exercising choice. If females prefer extreme male traits because they indicate male genetic quality that will enhance the fitness of offspring, a genetic correlation will evolve between female preference genes and genes that confer offspring fitness. We show that females of Drosophila serrata prefer extreme male cuticular hydrocarbon (CHC) blends, and that this preference affects offspring fitness. Female preference is positively genetically correlated with offspring fitness, indicating that females have gained genetic benefits from their choice of males. Despite male CHCs experiencing strong sexual selection, the genes underlying attractive CHCs also conferred lower offspring fitness, suggesting a balance between sexual selection and natural selection may have been reached in this population.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Quantum dynamics of two coupled qubits

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as nonpositive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. It is this feature that enables the quantum system to evolve to an entangled state. We conclude that the dynamics are a quantum element of nuclear magnetic resonance quantum-information processing. There are two limits where our quantum evolution coincides with the classical one: the short-time limit before spin-spin interaction sets in and the long-time limit when phase diffusion is incorporated.

The development of a positive non-infectious control for the detection of Perkinsus using the Ray test

To establish a noncontagious control for the Ray thioglycollate test for the detection of Perkinsus in mollusks we evaluated nonviable stages of P. olseni for enlargement of hypnospores and blue/black iodine stain. Trophozoites made nonviable with formalin, irradiation or colchicine failed to swell in thioglycollate. They remained small and did not differentially stain in iodine. Trophozoites that had already developed into hypnospores in thioglycollate were rendered inactive by freezing, ethanol or formalin immersion. They retained their iodinophilic properties and thus could provide a partial control for the Ray Test.