Characterization of distillability of entanglement in terms of positive maps

A necessary and sufficient condition for 1-distillability is formulated in terms of decomposable positive maps. As an application we provide insight into why all states violating the reduction criterion map are distillable and demonstrate how to construct such maps in a systematic way. We establish a connection between a number of existing results, which leads to an elementary proof for the characterisation of distillability in terms of 2-positive maps.Comment: 4 pages, revtex4. Published revised version, title changed, expanded discussion, main result unchange

Nuclear Spin Dynamics in Double Quantum Dots: Multi-Stability, Dynamical Polarization, Criticality and Entanglement

We theoretically study the nuclear spin dynamics driven by electron transport and hyperfine interaction in an electrically-defined double quantum dot (DQD) in the Pauli-blockade regime. We derive a master-equation-based framework and show that the coupled electron-nuclear system displays an instability towards the buildup of large nuclear spin polarization gradients in the two quantum dots. In the presence of such inhomogeneous magnetic fields, a quantum interference effect in the collective hyperfine coupling results in sizable nuclear spin entanglement between the two quantum dots in the steady state of the evolution. We investigate this effect using analytical and numerical techniques, and demonstrate its robustness under various types of imperfections.Comment: 35 pages, 19 figures. This article provides the full analysis of a scheme proposed in Phys. Rev. Lett. 111, 246802 (2013). v2: version as publishe

Observational and checklist measures of vocabulary composition: What do they mean?

Observational and checklist measures of vocabulary composition have both recently been used to look at the absolute proportion of nouns in children's early vocabularies. However, they have tended to generate rather different results. The present study is an attempt to investigate the relationship between such measures in a sample of 26 children between 1;1 and 2;1 at approximately 50 and 100 words. The results show that although observational and checklist measures are significantly correlated, there are also systematic quantitative differences between them which seem to reflect a combination of checklist, maternal-report and observational sampling biases. This suggests that, although both kinds of measure may represent good indices of differences in vocabulary size and composition across children and hence be useful as dependent variables in correlational research, neither may be ideal for estimating the absolute proportion of nouns in children's vocabularies. The implication is that questions which rely on information about the absolute proportion of particular kinds of words in children's vocabularies can only be properly addressed by detailed longitudinal studies in which an attempt is made to collect more comprehensive vocabulary records for individual children