Two-Qubit Separability Probabilities and Beta Functions

Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and quant-ph/0304041), exact formulas are available (both in terms of the Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and (n(n-1)/2-1)-dimensional volumes of the complex and real n x n density matrices. However, no comparable formulas are available for the volumes (and, hence, probabilities) of various separable subsets of them. We seek to clarify this situation for the Hilbert-Schmidt metric for the simplest possible case of n=4, that is, the two-qubit systems. Making use of the density matrix (rho) parameterization of Bloore (J. Phys. A 9, 2059 [1976]), we are able to reduce each of the real and complex volume problems to the calculation of a one-dimensional integral, the single relevant variable being a certain ratio of diagonal entries, nu = (rho_{11} rho_{44})/{rho_{22} rho_{33})$. The associated integrand in each case is the product of a known (highly oscillatory near nu=1) jacobian and a certain unknown univariate function, which our extensive numerical (quasi-Monte Carlo) computations indicate is very closely proportional to an (incomplete) beta function B_{nu}(a,b), with a=1/2, b=sqrt{3}in the real case, and a=2 sqrt{6}/5, b =3/sqrt{2} in the complex case. Assuming the full applicability of these specific incomplete beta functions, we undertake separable volume calculations.Comment: 17 pages, 4 figures, paper is substantially rewritten and reorganized, with the quasi-Monte Carlo integration sample size being greatly increase

Topological properties of quantum periodic Hamiltonians

We consider periodic quantum Hamiltonians on the torus phase space (Harper-like Hamiltonians). We calculate the topological Chern index which characterizes each spectral band in the generic case. This calculation is made by a semi-classical approach with use of quasi-modes. As a result, the Chern index is equal to the homotopy of the path of these quasi-modes on phase space as the Floquet parameter (\theta) of the band is varied. It is quite interesting that the Chern indices, defined as topological quantum numbers, can be expressed from simple properties of the classical trajectories.Comment: 27 pages, 14 figure

Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence

The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional and 15-dimensional in nature, respectively. The total volumes of the spaces they occupy with respect to the Hilbert-Schmidt and Bures metrics are obtainable as special cases of formulas of Zyczkowski and Sommers. We claim that if one could determine certain metric-independent 3-dimensional "eigenvalue-parameterized separability functions" (EPSFs), then these formulas could be readily modified so as to yield the Hilbert-Schmidt and Bures volumes occupied by only the separable two-qubit states (and hence associated separability probabilities). Motivated by analogous earlier analyses of "diagonal-entry-parameterized separability functions", we further explore the possibility that such 3-dimensional EPSFs might, in turn, be expressible as univariate functions of some special relevant variable--which we hypothesize to be the maximal concurrence (0 < C <1) over spectral orbits. Extensive numerical results we obtain are rather closely supportive of this hypothesis. Both the real and complex estimated EPSFs exhibit clearly pronounced jumps of magnitude roughly 50% at C=1/2, as well as a number of additional matching discontinuities.Comment: 12 pages, 7 figures, new abstract, revised for J. Phys.

Semi-classical study of the Quantum Hall conductivity

The semi-classical study of the integer Quantum Hall conductivity is investigated for electrons in a bi-periodic potential $V(x,y)$. The Hall conductivity is due to the tunnelling effect and we concentrate our study to potentials having three wells in a periodic cell. A non-zero topological conductivity requires special conditions for the positions, and shapes of the wells. The results are derived analytically and well confirmed by numerical calculations.Comment: 23 pages, 13 figure

Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems

We seek to derive the probability--expressed in terms of the Hilbert-Schmidt (Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit system is separable, by implementing the well-known Peres-Horodecki test on the partial transposes (PT's) of the associated 4 x 4 density matrices). But the full implementation of the test--requiring that the determinant of the PT be nonnegative for separability to hold--appears to be, at least presently, computationally intractable. So, we have previously implemented--using the auxiliary concept of a diagonal-entry-parameterized separability function (DESF)--the weaker implied test of nonnegativity of the six 2 x 2 principal minors of the PT. This yielded an exact upper bound on the separability probability of 1024/{135 pi^2} =0.76854$. Here, we piece together (reflection-symmetric) results obtained by requiring that each of the four 3 x 3 principal minors of the PT, in turn, be nonnegative, giving an improved/reduced upper bound of 22/35 = 0.628571. Then, we conclude that a still further improved upper bound of 1129/2100 = 0.537619 can be found by similarly piecing together the (reflection-symmetric) results of enforcing the simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors. In deriving our improved upper bounds, we rely repeatedly upon the use of certain integrals over cubes that arise. Finally, we apply an independence assumption to a pair of DESF's that comes close to reproducing our numerical estimate of the true separability function.Comment: 16 pages, 9 figures, a few inadvertent misstatements made near the end are correcte

Sensory-based niche partitioning in a multiple predator-multiple prey community

Many predators and parasites eavesdrop on the communication signals of their prey. Eavesdropping is typically studied as dyadic predator-prey species interactions; yet in nature, most predators target multiple prey species and most prey must evade multiple predator species. The impact of predator communities on prey signal evolution is not well understood. Predators could converge in their preferences for conspicuous signal properties, generating competition among predators and natural selection on particular prey signal features. Alternatively, predator species could vary in their preferences for prey signal properties, resulting in sensory-based niche partitioning of prey resources. In the Neotropics, many substrate-gleaning bats use the mate-attraction songs of male katydids to locate them as prey. We studied mechanisms of niche partitioning in four substrate- gleaning bat species and found they are similar in morphology, echolocation signal design and prey-handling ability, but each species preferred different acoustic features of male song in 12 sympatric katydid species. This divergence in predator preference probably contributes to the coexistence of many substrate-gleaning bat species in the Neotropics, and the substantial diversity in the mate-attraction signals of katydids. Our results provide insight into how multiple eavesdropping predator species might influence prey signal evolution through sensory-based niche partitioning

Neural correlates of sexual cue reactivity in individuals with and without compulsive sexual behaviours

Although compulsive sexual behaviour (CSB) has been conceptualized as a "behavioural" addiction and common or overlapping neural circuits may govern the processing of natural and drug rewards, little is known regarding the responses to sexually explicit materials in individuals with and without CSB. Here, the processing of cues of varying sexual content was assessed in individuals with and without CSB, focusing on neural regions identified in prior studies of drug-cue reactivity. 19 CSB subjects and 19 healthy volunteers were assessed using functional MRI comparing sexually explicit videos with non-sexual exciting videos. Ratings of sexual desire and liking were obtained. Relative to healthy volunteers, CSB subjects had greater desire but similar liking scores in response to the sexually explicit videos. Exposure to sexually explicit cues in CSB compared to non-CSB subjects was associated with activation of the dorsal anterior cingulate, ventral striatum and amygdala. Functional connectivity of the dorsal anterior cingulate-ventral striatum-amygdala network was associated with subjective sexual desire (but not liking) to a greater degree in CSB relative to non-CSB subjects. The dissociation between desire or wanting and liking is consistent with theories of incentive motivation underlying CSB as in drug addictions. Neural differences in the processing of sexual-cue reactivity were identified in CSB subjects in regions previously implicated in drug-cue reactivity studies. The greater engagement of corticostriatal limbic circuitry in CSB following exposure to sexual cues suggests neural mechanisms underlying CSB and potential biological targets for interventions

Exploring how a genetic attribution to disease relates to stigma experiences of Xhosa patients with schizophrenia in South Africa

Background: Over the past three decades, a range of international stakeholders have highlighted the possibility that genomic research may impact stigma associated with psychiatric disorders. Limited research has been conducted in Africa to investigate this relation. Method In the present study, using focus group discussions, we explored the relation between genetic attribution and stigma among 36 Xhosa people with schizophrenia. We addressed three main questions: (1) What causal beliefs do Xhosa people with schizophrenia use to explain their illness and to what extent do genetic explanations play a role in these beliefs? (2) What are the internalised stigma experiences of Xhosa people with schizophrenia? (3) How do genetic explanations relate to stigma experiences, if at all? Results Most participants were able to define genetics and some linked genetics to disease causation. Despite adequate knowledge of genetics and an emphasis on genetic explanations of schizophrenia in the study, most participants held a multitude of causal explanations including: psychosocial, environmental, and cultural. Moreover, participants rarely mentioned disease cause when describing their stigma experiences. Discussion For this population group, there was no straight-forward relation between a genetic attribution and stigma. Therefore, we did not fnd evidence that genetic attribution may signifcantly increase stigma. Although North American and European literature provides conficting evidence regarding this relation, there is increased consensus that biomedical explanations for psychiatric disorders may reduce blame. This study found evidence supporting that consensus. This study provides an empirical foundation to inform ongoing work on the psychosocial implications of psychiatric genomics research in non-Western contexts

Matched sizes of activating and inhibitory receptor/ligand pairs are required for optimal signal integration by human Natural Killer cells

It has been suggested that receptor-ligand complexes segregate or co-localise within immune synapses according to their size, and this is important for receptor signaling. Here, we set out to test the importance of receptor-ligand complex dimensions for immune surveillance of target cells by human Natural Killer (NK) cells. NK cell activation is regulated by integrating signals from activating receptors, such as NKG2D, and inhibitory receptors, such as KIR2DL1. Elongating the NKG2D ligand MICA reduced its ability to trigger NK cell activation. Conversely, elongation of KIR2DL1 ligand HLA-C reduced its ability to inhibit NK cells. Whereas normal-sized HLA-C was most effective at inhibiting activation by normal-length MICA, only elongated HLA-C could inhibit activation by elongated MICA. Moreover, HLA-C and MICA that were matched in size co-localised, whereas HLA-C and MICA that were different in size were segregated. These results demonstrate that receptor-ligand dimensions are important in NK cell recognition, and suggest that optimal integration of activating and inhibitory receptor signals requires the receptor-ligand complexes to have similar dimensions

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns