Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of error-correction dis
tinguished by different orthogonal vector subspaces, the coset subspaces. Moreover, the generated codes can be classified into four types with respect to the spinors in the unitary Lie algebra and a chosen initial quantum state.
In this report, a scheme different from the PT and Wootters concurrence is developed to acquire a criterion to investigate the bipartite separability of the Werner state.
A decomposition form is introduced in this report to establish a criterion for the bi-partite separability of Bell diagonal states. A such criterion takes a quadratic form of the coefficients of a given Bell diagonal states and can be derived via a s
imple algorithmic calculation of its invariants. In addition, the criterion can be extended to a quantum system of higher dimension.
