The Application Of Semidefinite Programming In The Study Of Multiparticle Genuine Entanglement

Semidefinite programming particularly the linear semi-definite programming is an important method which can calculate a linear functions maximize (minimize) values under the constraint that an affine combination of symmetic matrices is positive semidefinite. This constraint is convex but not linear and smooth, we also define it as nonsmooth convex optimization problems. semidefinite programming got the favour of people based on its applications in numerous fields and its mature interior-point calculate methods.In the field of quantum information, multiparticle entanglement especially the genuine multiparticle entanglement is viewed as a resource, and people are interested in studying it. The distinction between general quantum state and quantum state transformation are semidefinite programming problems. Semidefinite programming problem is a convex optimization problems, which can guarantee the solution to the global optimal solution. In this situation we translate the problem of quantum entanglement into the style of the semidefinite programming and then detect it genuine multiparticle entanlement.In the information field especially in the process of information transmission, noise is unavoidable. So in this paper, we are mainly studied the following questions. The genuine entanlement detection of quantum states mixed with white noise. We know that in quantum information transmission, it also exist channel noise.That we have studied the genuine multiparticle entanlement of the state through the quantum noise channel. We are focus on the combined amplitude damping and dephasing channel and pauli channel. The quantum states we are mainly studied is GHZ state, W state, W’state and superposition of them.