Controlled Teleportation And Controlled Dense Coding

We steady the controlled teleportation and controlled dense coding with W state, GHZ state and cluster state, respectively. It is shown that the successful probabilities of controlled teleportation with GHZ state and cluster state are 1, while the one with W state is 2/3. We discuss the controlled dense coding with GHZ and GHZ-class state, respectively, in chapter four, and find that the average amount of information different with different purifications, and put forwards another scheme how to realize the controlled dense coding with POVMs, instead of purifing the state. In addition, we investigate the entanglement of superposition of multi-states, and explore the relations between the entanglement of superposition and the entanglements of the superposed states. In finally, we investigate probabilistic coding of quantum states of different dimensions, and give a formula for calculating the average probability of successful decoding.