Graph state basis for Pauli Channels

We introduce graph state basis diagonalization to calculate the coherent information of a quantum code passing through a Pauli channel. The scheme is 5000 times faster than the best known one for some concatenated repetition codes, providing us a practical constructive way of approaching the quantum capacity of a Pauli channel. The calculation of the coherent information of non-additive quantum code can also be greatly simplified in graph state basis.Comment: 5 page

Contributions of natural and human factors to increases in vegetation productivity in China

Increasing trends in vegetation productivity have been identified for the last three decades for many regions in the northern hemisphere including China. Multiple natural and human factors are possibly responsible for the increases in vegetation productivity, while their relative contributions remain unclear. Here we analyzed the long-term trends in vegetation productivity in China using the satellite-derived normalized difference vegetation index (NDVI) and assessed the relationships of NDVI with a suite of natural (air temperature, precipitation, photosynthetically active radiation (PAR), atmospheric carbon dioxide (CO2) concentrations, and nitrogen (N) deposition) and human (afforestation and improved agricultural management practices) factors. Overall, China exhibited an increasing trend in vegetation productivity with an increase of 2.7%. At the provincial scale, eleven provinces exhibited significant increases in vegetation productivity, and the majority of these provinces are located within the northern half of the country. At the national scale, annual air temperature was most closely related to NDVI and explained 36.8% of the variance in NDVI, followed by afforestation (25.5%) and crop yield (15.8%). Altogether, temperature, total forest plantation area, and crop yield explained 78.1% of the variance in vegetation productivity at the national scale, while precipitation, PAR, atmospheric CO2 concentrations, and N deposition made no significant contribution to the increases in vegetation productivity. At the provincial scale, each factor explained a part of the variance in NDVI for some provinces, and the increases in NDVI for many provinces could be attributed to the combined effects of multiple factors. Crop yield and PAR were correlated with NDVI for more provinces than were other factors, indicating that both elevated crop yield resulting from improved agricultural management practices and increasing diffuse radiation were more important than other factors in increasing vegetation productivity at the provincial scale. The relative effects of the natural and human factors on vegetation productivity varied with spatial scale. The true contributions of multiple factors can be obscured by the correlation among these variables, and it is essential to examine the contribution of each factor while controlling for other factors. Future changes in climate and human activities will likely have larger influences on vegetation productivity in China