Using Measurement And Feedback To Manipulate Quantum State Against Decoherence

In recent years, the rapid development of quantum information has attracted a lot ofattention. The efficiency of actual quantum information processing depends crucially onquantum coherence and entanglement. But due to the inevitable interaction between a quan-tum system and its surrounding environment, decoherence will happen, which is the mainobstacle for realizing quantum information tasks. In this thesis, we mainly investigate how touse quantum measurement and feedback control to manipulate quantum states against deco-herence, and the entire thesis consists of the following three parts.In the first part, we consider a quantum system interacting with a bath and derive a mas-ter equation in the Lindblad form describing the evolution of the whole system consisting ofthe open quantum system and its surrounding environment subjected to a measurement-baseddirect quantum feedback control. We choose a model of a qubit coupled with a dephasingenvironment under the measurement-based feedback control. And we show that for any givenpure target state we can always find the corresponding measurement-based feedback scheme,which can effectively drive any initial state into this target state. By using an appropriate feed-back scheme with weak measurement, we can also stabilize a single qubit initially preparedin one of two nonorthogonal states against dephasing noise. Furthermore, we can effectivelyprotect a kind of known mixed states composed of two nonorthogonal states by using thecorresponding measurement-based feedback scheme.In the second part, we propose an extended master equation for the dynamics of thereduced system in the presence of measurement-based feedback control. Two prototypicalclasses of decoherence channels are considered: phase damping and generalized amplitudedamping. For a qubit system subjected to one of the noise channels, we analytically solve thismaster equation and obtain the solution of the state vector dynamics. Based on the state vectordynamics, we realize the preparation of an arbitrary quantum pure state by using appropriatemeasurement-based feedback scheme, and we also compare the effects of preparation underdifferent noise channels. Furthermore, we also study how to protect two nonorthogonal statesunder each of the noise channel, and find that projective measurement with unbiased basis is not optimal for this task, while weak measurement with biased basis could realize the bestprotection of two nonorthogonal states.In the last part, we consider that two qubits interact with a common structured reservoirand initially there are correlations between the qubit system and the reservoir. By performinglocal measurements before and after the two qubits undergo decoherence, not only more en-tanglement can be produced between them at the beginning, but also the produced entangle-ment can sustain much longer time. We focus on investigating the effects of different initialsystem-environment correlations on the entanglement of the system qubits, and in each case,we obtain the optimal pre-and post-measurement strength that give the maximum amount ofentanglement of the two qubits against decoherence. We find that the initial quantum corre-lations would induce much more entanglement than the initial classical correlations, and theinduced entanglement can preserve longer time in the initial quantum correlation case. Theenhancement of the entanglement depends on the evolution time, the decay rate and the initialstate.