Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum systems. It is shown that this criterion can be better than the previous ones in detecting entanglement. The results are generalized to multipartite quantum states.
We study the equivalence of mixed states under local unitary transformations in bipartite system and three partite system. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed in terms of the products, trace and determinant of matrices. This method and results can be extended to multipartite high dimensional system.
We study the trade-off relations on the maximal violation of CHSH tests for the multi-qubit pure states. Firstly, according to the classification of 3-qubit pure states under stochastic local operations and classical communication, four trade-off relations on CHSH tests are provided. The process of proof also provides the method of calculating its exact value. Then we consider the multi-qubit quantum systems, and we prove that the conjecture in [PRA 94, 042105 (2016)] is right for some special 4-qubit or more qubit pure states.
In order to discuss the relationship of the property and efficacy, according to relevant literature, the study found that it did not make a clear summary of the relationship between the property and efficacy of Chinese Medicine. And currently, the traditional Chinese Medicine theory is limited to the understanding of the traditional Chinese Medicine. It is difficult to break through the limitations. This discussion found that the property of a medicine and efficacy have a cause-effect relation. Furthermore, the efficacy of Chinese Medicine is one of the core theories.
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