Research On The Decoherence Suppression And The Entanglement Control Of The Open Quantum Systems

Quantum coherence and quantum entanglement are the bases of the quantum tech-nologies. They will usually be destroyed by the decoherence induced by environmentalinteractions, which has become the main obstacle for the implementation of the quan-tum technologies. Therefore, it is of great importance to suppress the decoherence.The thesis discusses the decoherence suppression and the corresponding entanglementcontrol problems with the help of the coherence vector representation of the densitymatrix. The main contributions are as follows:(1) The decoherence suppression of N level Markovian systems is investigatedby the optimal control in the coherence vector representation. The N level Markoviansystem can be described by the master equation, and possesses a standard bilinear formin the coherence vector representation. For this bilinear system, the optimal trajectorytracking method is used to suppress the decoherence effects brought by the environ-mental noises. It is shown that, when the system satisfies the complete decoherenceconditions, the controllability and the convergence assumptions, the optimal controlstrategy gives good results. The optimal trajectories asymptotically synchronize withthe oscillating free-evolution trajectories with partial loss of the amplitudes, and theoptimal control laws are asymptotically sinusoidal signals that are easy to be realizedin the laboratory. For some special cases when the optimal control works badly, thefeedback control strategy is introduced to retrieve the effectiveness of the optimal con-trol.(2) In the coherence vector representation, the concept of the noise decoupling de-composition of the Lie algebra su(N) is introduced and applied to completely decouplea part of the variables in the coherence vector from the environmental noises. Basedon the first noise decoupling decomposition of su(N), it is shown that some variablesin the coherence vector of the N level systems can be asymptotically decoupled fromthe environments via the open-loop controls. On the other hand, based on the secondnoise decoupling decomposition of su(N), feedback control laws can be designed toexactly decouple some variables from the environments, and they are not affected bythe possible transitional processes.(3) The decoherence control of non-Markovian systems is explored. The conceptof the intermediate"bath"is introduced here. In this model, the total system of thesystem plus the bath can be described by a master equation. The simulation exhibitssimilar oscillating trajectories that asymptotically synchronize with the object trajecto-ries, and the control laws are asymptotically sinusoidal signals.(4) The quantum entanglement as a typical quantum phenomenon is studied.Firstly, a new entanglement measure is proposed. Compared with the existing entan-glement measures, this measure is applicable to a wider class of quantum states and canbe analytically expressed in terms of the coherence vector. Based on this measure, theproblem of the entanglement preservation is discussed combined with the former pro-posed decoherence suppression strategies. Generally, the entanglement can be partiallypreserved. Even better, for the two-qubit case, the entanglement can be completelypreserved in an asymptotic manner.The last part summarizes the results obtained in the thesis and the further researchdirections are pointed out.