Discrete phase-space structure of nn-qubit mutually unbiased bases

We work out the phase-space structure for a system of $n$ qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field \Gal{2^n} and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for $n$ qubits.Comment: Title changed. Improved version. Accepted for publication in Annals of Physic

Unpolarized states and hidden polarization

We capitalize on a multipolar expansion of the polarisation density matrix, in which multipoles appear as successive moments of the Stokes variables. When all the multipoles up to a given order $K$ vanish, we can properly say that the state is $K$th-order unpolarized, as it lacks of polarization information to that order. First-order unpolarized states coincide with the corresponding classical ones, whereas unpolarized to any order tally with the quantum notion of fully invariant states. In between these two extreme cases, there is a rich variety of situations that are explored here. The existence of \textit{hidden} polarisation emerges in a natural way in this context.Comment: 7 pages, 3 eps-color figures. Submitted to PRA. Comments welcome

Uncertainty reconciles complementarity with joint measurability

The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary observables is proposed. The measured observables are represented as positive operator valued measures (POVMs), whose intrinsic fuzziness parameters are found to satisfy an intriguing pay-off relation reflecting the complementarity. At the same time, this relation represents an instance of a Heisenberg uncertainty relation for measurement imprecisions. A model-independent consideration show that this uncertainty relation is logically connected with the joint measurability of the POVMs in question.Comment: 4 pages, RevTeX. Title of previous version: "Complementarity and uncertainty - entangled in joint path-interference measurements". This new version focuses on the "measurement uncertainty relation" and its role, disentangling this issue from the special context of path interference duality. See also http://www.vjquantuminfo.org (October 2003

Quality of a Which-Way Detector

We introduce a measure Q of the "quality" of a quantum which-way detector, which characterizes its intrinsic ability to extract which-way information in an asymmetric two-way interferometer. The "quality" Q allows one to separate the contribution to the distinguishability of the ways arising from the quantum properties of the detector from the contribution stemming from a-priori which-way knowledge available to the experimenter, which can be quantified by a predictability parameter P. We provide an inequality relating these two sources of which-way information to the value of the fringe visibility displayed by the interferometer. We show that this inequality is an expression of duality, allowing one to trace the loss of coherence to the two reservoirs of which-way information represented by Q and P. Finally, we illustrate the formalism with the use of a quantum logic gate: the Symmetric Quanton-Detecton System (SQDS). The SQDS can be regarded as two qubits trying to acquire which way information about each other. The SQDS will provide an illustrating example of the reciprocal effects induced by duality between system and which-way detector.Comment: 10 pages, 5 figure

Theoretical Uncertainties in Red Giant Branch Evolution: The Red Giant Branch Bump

A Monte Carlo simulation exploring uncertainties in standard stellar evolution theory on the red giant branch of metal-poor globular clusters has been conducted. Confidence limits are derived on the absolute V-band magnitude of the bump in the red giant branch luminosity function (M_v,b) and the excess number of stars in thebump, R_b. The analysis takes into account uncertainties in the primordial helium abundance, abundance of alpha-capture elements, radiative and conductive opacities, nuclear reaction rates, neutrino energy losses, the treatments of diffusion and convection, the surface boundary conditions, and color transformations. The uncertainty in theoretical values for the red giant bump magnitude varies with metallicity between +0.13/-0.12 mag at [Fe/H] = -2.4 and +0.23/-0.21 mag at [Fe/H] = -1.0$. The dominant sources of uncertainty are the abundance of the alpha-capture elements, the mixing length, and the low-temperature opacities. The theoretical values of M_v,b are in good agreement with observations. The uncertainty in the theoretical value of R_b is +/-0.01 at all metallicities studied. The dominant sources of uncertainty are the abundance of the alpha-capture elements, the mixing length, and the high-temperature opacities. The median value of R_b varies from 0.44 at [Fe/H] = -2.4$ to 0.50 at [Fe/H] = -1.0. These theoretical values for R_b are in agreement with observations.Comment: 30 pages, 6 figures. To appear in Ap

The utility of twins in developmental cognitive neuroscience research: How twins strengthen the ABCD research design

The ABCD twin study will elucidate the genetic and environmental contributions to a wide range of mental and physical health outcomes in children, including substance use, brain and behavioral development, and their interrelationship. Comparisons within and between monozygotic and dizygotic twin pairs, further powered by multiple assessments, provide information about genetic and environmental contributions to developmental associations, and enable stronger tests of causal hypotheses, than do comparisons involving unrelated children. Thus a sub-study of 800 pairs of same-sex twins was embedded within the overall Adolescent Brain and Cognitive Development (ABCD) design. The ABCD Twin Hub comprises four leading centers for twin research in Minnesota, Colorado, Virginia, and Missouri. Each site is enrolling 200 twin pairs, as well as singletons. The twins are recruited from registries of all twin births in each State during 2006–2008. Singletons at each site are recruited following the same school-based procedures as the rest of the ABCD study. This paper describes the background and rationale for the ABCD twin study, the ascertainment of twin pairs and implementation strategy at each site, and the details of the proposed analytic strategies to quantify genetic and environmental influences and test hypotheses critical to the aims of the ABCD study. Keywords: Twins, Heritability, Environment, Substance use, Brain structure, Brain functio

Nitrogen restricts future sub-Arctic treeline advance in an individual-based dynamic vegetation model

Arctic environmental change induces shifts in high-latitude plant community composition and stature with implications for Arctic carbon cycling and energy exchange. Two major components of change in high-latitude ecosystems are the advancement of trees into tundra and the increased abundance and size of shrubs. How future changes in key climatic and environmental drivers will affect distributions of major ecosystem types is an active area of research. Dynamic vegetation models (DVMs) offer a way to investigate multiple and interacting drivers of vegetation distribution and ecosystem function. We employed the LPJ-GUESS tree-individual-based DVM over the Torneträsk area, a sub-Arctic landscape in northern Sweden. Using a highly resolved climate dataset to downscale CMIP5 climate data from three global climate models and two 21st-century future scenarios (RCP2.6 and RCP8.5), we investigated future impacts of climate change on these ecosystems. We also performed model experiments where we factorially varied drivers (climate, nitrogen deposition and [CO2]) to disentangle the effects of each on ecosystem properties and functions. Our model predicted that treelines could advance by between 45 and 195 elevational metres by 2100, depending on the scenario. Temperature was a strong driver of vegetation change, with nitrogen availability identified as an important modulator of treeline advance. While increased CO2 fertilisation drove productivity increases, it did not result in range shifts of trees. Treeline advance was realistically simulated without any temperature dependence on growth, but biomass was overestimated. Our finding that nitrogen cycling could modulate treeline advance underlines the importance of representing plant-soil interactions in models to project future Arctic vegetation change

Quantum concepts in optical polarization

We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored and their potential applications in quantum technologies are discussed