Information Transmission Through The Quantum Noisy Channel

Information science acts the great important part in improving the quality of people and promoting the development of the civilization of the society. However, with the people increasing desire for the capacity, speed, privacy and security of information transmission, and so on, the existing information system can not satisfy the requirement of people now. Therefore, a new subject——Quantum Information Theory—has been developed as the combination ofquantum mechanics and information theory. Quantum state is the carrier of quantum information. The process of preparation, operation, transmission andstorage of the quantum state are called quantum information process.How to reliably transmit the information through the quantum noisy channel is one of the important questions in quantum information theory. In this thesis, the information transmission through the quantum noisy channel is investigated by the quantum information theory. Our mainly work is as follows:1. The problem of sending a single classical bit through an amplitude-damping channel and a generalized amplitude damping channel is considered. When two transmissions through the channel are available as a resource, we find that two entangled transmissions can enhance the capability of receiver's judging information correctly under certain conditions compared with two product- state transmissions. In addition, for the generalized amplitude damping channel, we find a special case in which the two entangled transmissions can always make a classical bit more effectively disable the noise influence.2. The classical capacity of a generalized amplitude-damping channel is investigated by using a numerical method. It is shown that the classical capacity depends on the channel parameters representing the ambient temperature and dissipation. In particular, under a special condition, the classical capacity of the generalized amplitude-damping channel can be written as an analytical expression.3. The entanglement-assisted classical capacity of the generalized amplitude damping channel is investigated by using the properties of partial symmetry and concavity of mutual information. The numerical and analytical results of the entanglement-assisted classical capacity are obtained under some certain conditions. It is shown that, the entanglement-assisted classical capacity depends on the channel parameters representing the ambient temperature and dissipation, and the prior entanglement between sender and receiver can approximately double the classical capacity of the generalized amplitude damping channel.4. The problem of the classical information transmission through the Pauli channel with memory is investigated. A general formula for the mutual information of the Pauli channels with memory modeled by correlated noise is derived. It is shown that the mutual information depends on the channel shrinking factor, the input state parameter and the channel memory coefficient. The analyses based on the general formula reveal that the entanglement is always a useful resource to enhance the mutual information of some Pauli channels, such as the bit flip channel and the bit-phase flip channel. Our analyses also show that the entanglement is not advantageous to the reliable transmission of classical information for some Pauli channels at any time, such as the phase flip channel and the phase damping channel.