Certain Problems In Quantum Information Theory

The thesis combined our researches on Quantum information theory in past few years. The main content of this paper contains:First, bosonic gaussian channel's input-output fidelity, discrimination of qubits channels and classical capacity of a certain C-V channel. We give the exactly form of the fidelity for general bosonic Gaussian channels in cases channel's input be limited to Gaussian pure states. Besides, we discussed discrimination of qubit channels. At last using functional analysis and quantum transformation theory, we give the exact form of a certain C-V quantum channel's capacity; we also consider the tradeoff between the channel capacity and channel fidelity.Second, study on the adiabatic process of the time-dependent systems. we present the concepts of adiabatic orbit, adiabatic evolution orbit,U(1)-invariant adiabatic orbit and U(1)-invariant adiabatic evolution orbit. And we also reclaim the meanings of adiabatic evolution. Based on concept of U(1)-invariant adiabatic expansion we propose an invariant perturbation theory of quantum adiabatic process, furthermore, we obtain a new adiabatic condition. Besides, we find a new geometric quantity in adiabatic process, and we made some further researches on it.Third, Clone of mixed states. We pointed out that the optimal symmetric clone machine is not unique for mixed states. The conclusion is different from that Werner have proved in the case of pure states.And the Last, analysis on the entanglement construction of multi-party systems. We present a class theorem of multi-party entanglement construction and we discuss how to build entanglement of different construction.