Quantum teleportation is a very important problem in the process of quantum information. It plays an important role in quantum communication and quantum computation. Teleportation needs quantum channel and classical channel to transfer quantum and classical information respectively. The practical channels are unavoidably disturbed by noise. Therefore,with the robustness in our mind,we study the teleportation problems under nonideal conditions.In this thesis, we investingated the teleportation problems from three different aspeat. Firstly, we studied quantum teleportation problems when entangled channel are nonideal. Three kind of entangled channels are taken into consideration: EPR state,three-particle GHZ states and three-particle W-state. Secondly, we explore the antinoise ability of the above three channels on condition that the quantum channels are entangled and the classical channels are disturbed by noise, namely the robustness. Finally, we use semidefinite programming tools to design the optimal operation on condition that the quantum channels are mixed entangled states. The proposed algorithm achieves the maximal fidelity of teleportation.
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