Certain Problems In The Theory Of Quantum Channels

Quantum information theory, as a new rapidly emerging subject, its aim is to study the transmission of information in quantum physical systems. Quantum information theory fully takes advantages of the basic principles of quantum mechanics (quantum states overlapping principles) and basic concepts (quantum entanglement, for example)to carry out the processing of information. Although at current stages, quantum information theory still remains the original research of experimentalists and theorists, it provides a new angle and growing point for the practical applications of quantum theory. And the extensive researches will broaden and deepen quantum theory itself. Completely different from quantum mechanics, in quantum information theory what people exploit is quantum states themselves, and the task is to preserve, manipulate, transmitting and reading out the quantum states. We can prudently declare that the developments of quantum information theory could lead to a brand new quantum technology era.The initial quantum information processing schemes are only aimed at discrete variables (spins and polarizations, for example ) quantum systems (viz. qubits) For recent years, continuous variables (positions and momentums) quantum information processing proposals arouse wide concern. Continuous variables teleportation, entanglement swapping , quantum cloning, quantum computation, quantum error correction, entanglement purification have been put forth; we also come up with new quantum information schemes via continuous variable and discrete variable entanglement. With decades of development, quantum optics has become an mature and vigorous science. It provides some necessary sophisticated methods to verify certain fundamental problems in quantum mechanics. The outstanding characteristic of continuous variable quantum information processing is that: it can exploit linear optical devices (phase shifting and beam splitters, for example) to realize squeezed states; linear optical devices are easy to perform quantum operations with higher efficiency and precision. Hence, quantum optics provide applicable methods for various continuous variables quantum information schemes. However, in the experiments that testify Bell inequalities, people generally use discrete variable quantum systems. Applying non-degenerating optical parameter amplification, people can produce bimodal squeezed vacuum states, so as to realize the continuous variables (positions and momentums, for example) Einstein-Podolsky-Rosen paradox. On this basis, continuous variable quantum entanglement and nonlocality and their relations become great theoretical concern.This thesis contains four aspects of work:1. We use master equations to study quantum bosonic channels. And we give the exact form of the channel capacity and fidelity of noisy lossy bosonic channels.2. Using operators theory, we give the continuous variable teleportation qunatum channel its channel capacity and fidelity , and we have relevant discussions.3. We use relative entropy to distinguish discrete variable and continuous variable quantum channels.4. We study the mechanism of the fidelity of various Gaussian channels.