Mathematical Description Of Quantum Teleportation

With the growing demand for information, people are constantly promoting the Informa-tion Science and Technology. Quantum Information Science and Technology refers to a subject combined by quantum mechanics, information science and computer science, the most basic element is quantum entanglement property. Quantum teleportation is an important part of quantum information science. Using the quantum entanglement property, this paper studies the controlled quantum teleportation.Quantum teleportation means that, via pre-established quantum and classical channels, making a certain quantum operation. Through the combined effect of the quantum and classical channels, the quantum state of the particles can be transferred to the particles on the other side of the quantum channel. In this process, what was transferred is the quantum state of the particle, while the particle itself and it’s location wouldn’t be changed.How to choose the best quantum channel in controlled quantum teleportation of two-particle entangled state is discussed in this thesis. Using four-particle GHZ state and four-particle special "anti-correlating GHZ state "as quantum channels respectively, two controlled quantum teleportation schemes of anti-correlating entangled state are presented. The concrete matrix formations of unitary transformations adopted by the receiver are compared in the two schemes, and the relationship between the quantum entangled state and quantum channel is analyzed. Then the best quantum channels of correlating entangled state and anti-correlating entangled state are proposed, which are four-particle GHZ state and four-particle special "anti-correlating GHZ state" respectively.This paper also discusses the application of the optimal quantum channel in the probably teleportation of the two particle anti-correlating entangled state. It is different from the other scheme in that the implementation of the unitary transformation in the end to get the particles is simpler than that of the other quantum channels.