Quantum Secret Sharing And The Nonlocality Of High Dimensional Entangled Mixed States

It shows the application of quantum mechanics in information transimssion and computation. It supplies a powerful tool for secure communication and speeding up the computation of mathematic problems. Quantum communication is one of the two important branches of quantum information and had achieved great progress both in theory and experiment in the recent years. It has attracted a lot of attention.In this dissertation, after a brief review of quantum mechanics, the author first introduces the basic knowledge of quantum information, and then discusses some branches of quantum information, including quantum teleportation, quantum secret sharing, quantum nonlocality and quantum entanglement swapping, which are related to her researches during the study toward a Ph.D. degree.In quantum teleportation, we present two different models. The first one is a quantum teleportation scheme based on pure entangled states. It can be used to teleport an arbitrary GHZ-class state with a pure entangled two-particle quantum channel and has the advantage of transmitting much less particles than others. The second one is an optimal multiparty-controlled teleportation scheme based on nonmaximal entangled states. The scheme is optimal as the probability that the receiver obtains the originally state equals the entanglement of the quantum channel. Moreover, it gives out an optimal evolution for obtaining the unknown state with only an auxiliary two-level quantum system.In quantum secret sharing, we present a scheme for multiparty quantum secret sharing with pure entangled states and decoy photons. It uses the decoy photons to prevent a potentially dishonest agent from eavesdropping freely. This scheme does not require the parties of communication to have an ideal entangled quantum source, which makes it more convenient than others in a practical application. The second one is a three-party quantum secret sharing scheme with single photons. It uses two nonorthogonal photon states to realize quantum secret sharing and has the advantage of having a high intrinsic efficiency for qubits.Although quantum nonlocality has attracted a lot of attention recently, there are a lot of open questions in the nonlocality of d-dimensional quantum system, especially in a mixed state. In the case of d-dimensional quantum system, we present a class of mixed states which can be used for nonlocality proof. According to PPT separability condition, it is an entangled state, however, not all entangled states can be used for nonlocality proof.In quantum entanglement swapping, we present a scheme for an arbitrary d-dimensional quantum entanglement swapping with a pure entangled state.