Largest separable balls around the maximally mixed bipartite quantum state

For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of separable (unentangled) matrices around the identity matrix. This implies a simple and intutively meaningful geometrical sufficient condition for separability of bipartite density matrices: that their purity \tr \rho^2 not be too large. Theoretical and experimental applications of these results include algorithmic problems such as computing whether or not a state is entangled, and practical ones such as obtaining information about the existence or nature of entanglement in states reached by NMR quantum computation implementations or other experimental situations.Comment: 7 pages, LaTeX. Motivation and verbal description of results and their implications expanded and improved; one more proof included. This version differs from the PRA version by the omission of some erroneous sentences outside the theorems and proofs, which will be noted in an erratum notice in PRA (and by minor notational differences

Micronutrients deficiency and associated sociodemographic factors in Chinese children

Background: Although the prevalence of malnutrition has decreased, micronutrient deficiency still exists among children. While iron level has been studied, limited information on serum levels of zinc in Chinese children is available. This study aims to describe the status of micronutrients and its association with sociodemographic factors, and to assess associated risk factors. Methods: A cross-sectional study was performed on 1375 Chinese preschool children. Venous blood samples were collected and analyzed for zinc and iron by atomic absorption spectrophotometry. Sociodemographic information was obtained from self-administered questionnaires given to the parents. Results: The high prevalence of low serum zinc (38.2%) and iron (24.3%) was found. Children from rural preschools had the lowest zinc levels, whereas those from urban preschools had the lowest iron levels. Children living in small houses had the highest prevalence of low serum zinc (47.1%), and children from small families (≤3 persons) had a higher prevalence of low serum zinc than those from large families (41.8% vs. 34.1%). Conclusions: Our findings in the recent socioeconomic development of China suggest the need for continuous monitoring of nutritional factors and highlight the importance of public health implication in preschool children even in developed regions.Jianghong Liu, Yue-Xian Ai, Alexandra Hanlon, Zumin Shi, Barbra Dickerman and Charlene Comphe