Study On The Feedback-based Control Of Quantum States

In quantum information, quantum coherence and entanglement have attracted much attention. Because of the interactions between different quantum systems and the couplings between the quantum systems and their and environments, quantum coherence and quantum entanglement will deteriorate unavoidably. Meanwhile, the efficiencies of the practical quantum processing protocols are depending on the quantum coherence and quantum entanglement. So how to maintain the quantum coherence and quantum entanglement becomes more and more important. In this thesis, we are going to transplant the feedback techniques of the classical control theory into the quantum control system, i.e. the quantum feedback method is adopted to realize the manipulation and protection of quantum coherence and quantum entanglement. Because of the effects of environments, how to solve the quantum master equation become crucial for this thesis. In general, the analytical solution of master equation is not easy, so we will use the numerical method to solve the master equation and get the evolutions of the quantum coherence and entanglement of the quantum systems. In addition, the entangled states created under noisy environments are usually mixed states, which is not the ideal physical resource for quantum information processing. In this thesis, we will consider the problem of how to generate a pure entangled state in the open systems. Based on the above mentioned studies, we got several valuable results as follows:1. Feedback-based modification of the evolutions of quantum coherence and entanglement of open quantum systems. Based on quantum feedback techniques and numerical simulation methods, we studied the quantum coherence dynamics and quantum entanglement dynamics of open quantum systems. Here, we focus on the effects of the initial states and the feedback Hamiltonians on the coherence dynamics and the entanglement dynamics. The detection efficiency is supposed to be unit here, and the case of the non-unit detection efficiency has also been discussed a bit. The results show that, the appropriate feedback Hamiltonian can protect the quantum coherence and quantum entanglement of the open quantum systems. The key point here is how to design the optimal feedback Hamiltonian for the corresponding initial state. We gave a detailed discuss on this point in the thesis, which is of great importance for overcoming decoherence and disentanglement.2. Creation of pure tripartite entangled states under noisy environments. Firstly, we introduced and gave detailed discussion of the theory presented by Yamamoto to for the generation of pure Bell states under noises. Based on the combination of the Homodyne-mediated local feedback and global feedback, we designed a generation scheme for the pure tripartite maximally entangled states of open quantum systems, such as, the GHZ state and the W state. Because the practical quantum systems are all inside its environments, and the pure multipartite entanglement is crucial for quantum communication and quantum computation, the study of the generation of pure multipartite entanglement between open quantum systems are of great importance for the development of the experimental quantum information.