Bell's Inequality and Entanglement in Qubits

We propose an alternative evaluation of quantum entanglement by measuring the maximum violation of the Bell's inequality without performing a partial trace operation. This proposal is demonstrated by bridging the maximum violation of the Bell's inequality and the concurrence of a pure state in an $n$-qubit system, in which one subsystem only contains one qubit and the state is a linear combination of two product states. We apply this relation to the ground states of four qubits in the Wen-Plaquette model and show that they are maximally entangled. A topological entanglement entropy of the Wen-Plaquette model could be obtained by relating the upper bound of the maximum violation of the Bell's inequality to the concurrences of a pure state with respect to different bipartitions.Comment: 10 page

Establishing National Carbon Emission Prices for China

The purpose of the paper is to establish national carbon emissions prices for the People’s Republic of China, which is one of the world’s largest producers of carbon emissions. Several measures have been undertaken to address climate change in China, including the establishment of a carbon trading system. Since 2013, eight regional carbon emissions markets have been established, namely Beijing, Shanghai, Guangdong, Shenzhen, Tianjin, Chongqing, Hubei and Fujian. The Central Government announced a national carbon emissions market, with power generation as the first industry to be considered. However, as carbon emissions prices in the eight regional markets are very different, for a variety of administrative reasons, it is essential to create a procedure for establishing a national carbon emissions price. The regional markets are pioneers, and their experience will play important roles in establishing a national carbon emissions market, with national prices based on regional prices, turnovers and volumes. The paper considers two sources of regional data for China’s carbon allowances, which are based on primary and secondary data sources, and compares their relative strengths and weaknesses. The paper establishes national carbon emissions prices based on the primary and secondary regional prices, for the first time, and compares both national prices and regional prices against each other. The carbon emission prices in Hubei, Guangdong, Shenzhen and Tianjin are highly correlated with the national prices based on the primary and secondary sources. Establishing national carbon emissions prices should be very helpful for the national carbon emissions market that is under construction in China, as well as for other regions and countries worldwide

Hanle-effect measurements of spin injection from Mn5Ge3C0.8/Al2O3-contacts into degenerately doped Ge channels on Si

We report electrical spin injection and detection in degenerately doped n-type Ge channels using Mn5Ge3C0.8/Al2O3/n^{+}-Ge tunneling contacts for spin injection and detection. The whole structure is integrated on a Si wafer for complementary metal-oxide-semiconductor compatibility. From three-terminal Hanle-effect measurements, we observe a spin accumulation up to 10 K. The spin lifetime is extracted to be 38 ps at T = 4K using Lorentzian fitting, and the spin diffusion length is estimated to be 367 nm due to the high diffusion coefficient of the highly doped Ge channel.Comment: 5 pages, 4 figure