Mutually unbiased bases: tomography of spin states and star-product scheme

Mutually unbiased bases (MUBs) are considered within the framework of a generic star-product scheme. We rederive that a full set of MUBs is adequate for a spin tomography, i.e. knowledge of all probabilities to find a system in each MUB-state is enough for a state reconstruction. Extending the ideas of the tomographic-probability representation and the star-product scheme to MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin states and operators are introduced, ordinary and dual star-product kernels are found. Since MUB-projectors are to obey specific rules of the star-product scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new relations on triple- and four-products of MUB-projectors. Example of qubits is considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is discussed.Comment: 11 pages, 1 table, partially presented at the 17th Central European Workshop on Quantum Optics (CEWQO'2010), June 6-11, 2010, St. Andrews, Scotland, U

Pauli Diagonal Channels Constant on Axes

We define and study the properties of channels which are analogous to unital qubit channels in several ways. A full treatment can be given only when the dimension d is a prime power, in which case each of the (d+1) mutually unbiased bases (MUB) defines an axis. Along each axis the channel looks like a depolarizing channel, but the degree of depolarization depends on the axis. When d is not a prime power, some of our results still hold, particularly in the case of channels with one symmetry axis. We describe the convex structure of this class of channels and the subclass of entanglement breaking channels. We find new bound entangled states for d = 3. For these channels, we show that the multiplicativity conjecture for maximal output p-norm holds for p=2. We also find channels with behavior not exhibited by unital qubit channels, including two pairs of orthogonal bases with equal output entropy in the absence of symmetry. This provides new numerical evidence for the additivity of minimal output entropy

Superconductivity in the SU(N) Anderson Lattice at U=\infty

We present a mean-field study of superconductivity in a generalized N-channel cubic Anderson lattice at U=\infty taking into account the effect of a nearest-neighbor attraction J. The condition U=\infty is implemented within the slave-boson formalism considering the slave bosons to be condensed. We consider the $f$-level occupancy ranging from the mixed valence regime to the Kondo limit and study the dependence of the critical temperature on the various model parameters for each of three possible Cooper pairing symmetries (extended s, d-wave and p-wave pairing) and find interesting crossovers. It is found that the d- and p- wave order parameters have, in general, very similar critical temperatures. The extended s-wave pairing seems to be relatively more stable for electronic densities per channel close to one and for large values of the superconducting interaction J.Comment: Seven Figures; one appendix. Accepted for publication in Phys. Rev.

Aharonov-Anandan Effect Induced by Spin-Orbit Interaction and Charge-Density-Waves in Mesoscopic Rings

We study the spin-dependent geometric phase effect in mesoscopic rings of charge-density-wave(CDW) materials. When electron spin is explicitly taken into account, we show that the spin-dependent Aharonov-Casher phase can have a pronounced frustration effects on such CDW materials with appropriate electron filling. We show that this frustration has observable consequences for transport experiment. We identify a phase transition from a Peierls insulator to metal, which is induced by spin-dependent phase interference effects. Mesoscopic CDW materials and spin-dependent geometric phase effects, and their interplay, are becoming attractive opportunities for exploitation with the rapid development of modern fabrication technology.Comment: 5 pages, 6 figures, to appear in Phys.Rev.B(Aug.15, 1998

Randomized Trials to Optimize Treatment of Multidrug-Resistant Tuberculosis: The time for action is now

The time is now right for randomized trials of MDR-TB, say the authors, as the expansion of MDR-TB programs provides the setting in which trials can be implemented

One-mode Bosonic Gaussian channels: a full weak-degradability classification

A complete degradability analysis of one-mode Gaussian Bosonic channels is presented. We show that apart from the class of channels which are unitarily equivalent to the channels with additive classical noise, these maps can be characterized in terms of weak- and/or anti-degradability. Furthermore a new set of channels which have null quantum capacity is identified. This is done by exploiting the composition rules of one-mode Gaussian maps and the fact that anti-degradable channels can not be used to transfer quantum information.Comment: 23 pages, 3 figure

Adherence to 24-Hour Movement Guidelines for the Early Years and associations with social-cognitive development among Australian preschool children

Background: The new Australian 24-Hour Movement Guidelines for the Early Years recommend that, for preschoolers, a healthy 24-h includes: i) ≥180 min of physical activity, including ≥60 min of energetic play, ii) ≤1 h of sedentary screen time, and iii) 10–13 h of good quality sleep. Using an Australian sample, this study reports the proportion of preschool children meeting these guidelines and investigates associations with social-cognitive development. Methods: Data from 248 preschool children (mean age = 4.2 ± 0.6 years, 57% boys) participating in the PATH-ABC study were analyzed. Children completed direct assessments of physical activity (accelerometry) and social cognition (the Test of Emotional Comprehension (TEC) and Theory of Mind (ToM)). Parents reported on children’s screen time and sleep. Children were categorised as meeting/not meeting: i) individual guidelines, ii) combinations of two guidelines, or iii) all three guidelines. Associations were examined using linear regression adjusting for child age, sex, vocabulary, area level socio-economic status and childcare level clustering. Results: High proportions of children met the physical activity (93.1%) and sleep (88.7%) guidelines, whereas fewer met the screen time guideline (17.3%). Overall, 14.9% of children met all three guidelines. Children meeting the sleep guideline performed better on TEC than those who did not (mean difference [MD] = 1.41; 95% confidence interval (CI) = 0.36, 2.47). Children meeting the sleep and physical activity or sleep and screen time guidelines also performed better on TEC (MD = 1.36; 95% CI = 0.31, 2.41) and ToM (MD = 0.25; 95% CI = −0.002, 0.50; p = 0.05), respectively, than those who did not. Meeting all three guidelines was associated with better ToM performance (MD = 0.28; 95% CI = −0.002, 0.48, p = 0.05), while meeting a larger number of guidelines was associated with better TEC (3 or 2 vs. 1/none, p < 0.02) and ToM performance (3 vs. 2, p = 0.03). Conclusions: Strategies to promote adherence to the 24-Hour Movement Behaviour Guidelines for the Early Years among preschool children are warranted. Supporting preschool children to meet all guidelines or more guidelines, particularly the sleep and screen time guidelines, may be beneficial for their social-cognitive development

Associations of common breast cancer susceptibility alleles with risk of breast cancer subtypes in BRCA1 and BRCA2 mutation carriers

Peer reviewedPublisher PD