Open Quantum State Manipulation Based On Quantum Measurements

Due to the interaction with the environment,a quantum state is subjected to decoherence which becomes one of the biggest problems for practical quantum computation.Quantum measurements can be used as the controls in the manipulation of quantum dynamics.In this thesis we use measurements and control operations to manipulate the state of the two level quantum system in different ways:1)Quantum state transfer control based on the optimal measurement.2)Quantum optimal noise suppression for pure initial states from phase damping via weak measurement.3)Quantum noise protection via weak measurement within a mixed state framework.1)We propose an optimal control of quantum state transfer in a two-dimensional quantum system by a sequence of non-selective projection measurements.We show that for a given initial state,one can always find the corresponding projection operator that can effectively drive the given initial state to any arbitrary target pure state.An external control is proposed to compensate the effect of the free evolution of system.Numerical simulations and characteristics analysis are given in three cases:without considering free evolution,considering free evolution,and with the action of external control field.The simulating experimental results show that the optimal measurement control is more effective by using proposed external control field.2)We present an optimal control scheme to correct a qubit in a two-level quantum system with an arbitrary pure initial state which is subjected to the phase damping.The control aim is to bring the qubit back as close as possible to its initial state.Strength-dependent measurements and control correction rotation in different bases are designed to protect the arbitrary pure state of qubit.We design the optimal measurement strength to achieve the best trade-off between the gaining system information,phase damping noise and the measure disturbance through measurement.Two cases are studied:(i)the value in initial states has y component,and(ii)the value in initial states does not have y component.We deduce the optimal parameters and performance of the control scheme for the various initial state situations.3)In addition,we discuss the possibility of protecting the mixed state of a quantum system that goes through noise by adaptive mcasurrments and control operations.The aim is to find the optimal measurement strength and control operations that makes the input and output states as close as possible.We show that our scheme can effectively protect arbitrary mixed state against typical types of noise sources:amplitude damping,phase damping and amplitude-phase damping.The optimal measurement and control operators are deduced in different bases of the Bloch sphere to find the best control scheme for each type of noise sources.The effectiveness of our control scheme is demonstrated by sim-ulation results.