The Determining Of Separable Quantum State

Quantum entanglement plays an increasingly more important role for many tasks in areas such as quantum informatics and national defense due to the potential that they can be performed faster in a more secure way than classical algorithms.It means that quantum entanglement can implement functions that classical algorithms cannot.Quantum entanglement has attracted worldwide attention and research since it was set up.The argument about it has never stopped.One of the fundamental problems concerning entanglement is the separability problem,i.e.,determining when a multipartite system can be untangled and how many items can be decomposed.However,the entanglement of highdimensional quantum systems remains a hard problem.In this paper we discuss the problem in bipartite system.At the risk of over simplifying the many elegant yet complex theory,this paper revisits some established knowledge and concentrates on the mathematical formulation of entanglement from classical linear algebra point of view.According to the hypothesis of the quantum mechanics,we define the density matrix,entangled state,separable state and the tensor product in Hilbert space.In this paper we discuss the problem in finite dimension bipartite system.The density matrix of separable quantum states is also separable.Separable density matrix form a convex set,it is natural to find the nearest separable state of a given generic state.Global optimization techniques are employed for the computation.Numerical experiments seem to confirm the performance of this approach.