Research On Several Basic Problems In Quantum Information Theory

Quantum information theory is the related areas of quantum mechanics and classical information theory. In this thesis, we study on several problems in quantum information theory, including the evolution of entanglement versus time as well as quantum teleportation and the purification of entangled state.In chapter 2, we propose four kinds' of schemes of quantum teleportation which are not reported before. Firstly, a scheme for teleporting a three-particle state is proposed by using three pairs of non-maximally entangled state particles as quantum channels. According this scheme, the sender Alice needs to make the Bell-state measurement three times and send the outcome to Bob by classical channel, then Bob may reconstruct the quantum states to be sended by Alice by using the corresponding unitary transformation. Secondly , we propose a scheme for probabilistically teleporting an unknown three-particle entangled state of three-level by means of a four-particle entangled state of three-level as quantum channel. First of all, the maximally entangled state is taken as quantum channel, then, the case of non-maximally entangled state is considered, we find that when the channel is non-maximally entangled state, by introducing an ancillary qubit and constructing an unitary transformation properly, the teleportation of three-particle entangled state can be accomplished with certain probability. Thirdly, we propose a scheme for teleporting an unknown three-particle entangled state of three-level by using entanglement swapping. In the process, the sender Alice needs to make the Bell-state measurement twice, then sends the outcome to Bob by classical channel, so Bob by means of the corresponding unitary transformation may reconstruct the quantum state which Alice wants to send. Fourthly, we propose a scheme for teleportation of a Schro|¨dinger cat-state by means of two-level atom-cavity state via the J-C model with large detuning. In the scheme, the ancillary particle is not needed, only a two-level atom and two single-model cavities are required.In chapter 3, we investigate the purification of entangled two-particle states and entangled three-particle states by means of entanglement swapping, and generalize it...