Quantum Teleportation And Quantum Channel

Quantum information science is an emerging subject based on the combination of quantum mechanics and information science. It mainly discusses the coherence of quantum state and its unique way of evolution in the field of information processing. The coherence of quantum state results in quantum entanglement in many-body quantum systems. The quantum entangled state can be viewed as a resource in quantum information science, because it can be used in many information processing schemes. Quantum teleportation is an example of the application of quantum entanglement, which shows that quantum information can be sent using quantum entanglement and classical communication. The evolution of quantum states can be seen as a channel, because it linked the quantum state before the evolution (input state) with the quantum state after the evolution (output state). When the quantum evolution is viewed as a quantum channel, from the perspective of the information theory, we can consider the problem of its capacity.Channel capacity problems are the most basic theoretical issues in the field of communication, because the channel capacity depicts the capability of that the communication channels reliably transmit information in a noisy environment. The proposition of Shannon noisy channel coding theorem has solved the problem of classical channel capacity. However, quantum channel capacity problem is more profound and more complex than classical channel capacity problem, because the quantum channel can be used not only to transmit classical information in the usual sense, but also to transmit the confidential classical information and quantum information. Therefore, the study of the information capacity of quantum channel (i.e., the classical capacity, private capacity and quantum capacity) has become the core theoretical problems in the field of quantum communication.The main contents of this paper related to the two aspects are as follows:First, we discuss quantum teleportation channel. The quantum teleportation process can also be seen as a channel, because it has an input state and an output state.The maximally entangled states as the entanglement resources can be used in the quantum teleportation process so that the output state and input state is completely consistent, indicating that at that time quantum teleportation channel without any noise. But when we use the general entangled states as the entanglement resources, the quantum teleportation channel is a noisy channel, because they do not always make the output state and input state exactly the same. We are the first to use the entanglement fidelity to depict the capability of a general quantum teleportation channel preserving quantum state. We calculated the entanglement fidelity of a general quantum teleportation channel when it is averaged on all input states, and obtained a very simple expression.Second, the classical channel capacity problem is discussed from the perspective of the quantum channel.Classical channel can be seen as a special quantum channel. Through the idea that the classical channel is viewed as a quantum channel, using the symbols of quantum mechanics, we give a proof of Shannon noisy classic channel coding theorem. Our proof simplifies the obscure parts of its classical argument and sets up a bridge between classical information theory and the rapid development of quantum information theory, which will be very useful for the classical information researchers who want to enter the field of quantum information.