On Quantum Manipulation In Quantum Information Processing

With the development of quantum technologies, the research domain of control sciences has been extended to the micro-world, and quantum control is becoming an important branch of control theory. It has been recognized that quantum control theory is a key step in the procedure of transforming quantum physics into quantum technologies. This thesis discusses the problem of quantum manipulation in quantum information processing from the following aspects: quantum measurement and manipulation of quantum states, controllability of quantum systems, decoherence control of quantum systems, and analysis of typical quantum systems. Main contributions are summarized as follows:(1) Quantum measurement and manipulation of quantum statesFirstly, we propose the concept of quantum generalized projector measurement (QGPM) and exploit the deterministic collapse property of QGPM. A scheme has been suggested to deterministically generate maximal entangled pure states by QGPM. Secondly, we extend the concept of QGPM and put forward the concept of quantum generalized subspace projector measurement (QGSPM). The collapse property of QGSPM is then explored and a scheme is obtained to deterministically create maximal entangled pure states by QGSPM. Finally, we discuss how to scalably construct Greenberger-Horne-Zeilinger(GWZ) states of multiple-qubit systems by Bell state measurements and analyze the resource cost of constructing these GHZ states.(2) Controllability of quantum systemsFirstly, we introduce the concept of subsystem controllability of quantum systems and derive a sufficient condition for the existence of controllable subsystems of open quantum systems. From the viewpoint of control theory, we explain why decoherence-free subsystems can be used for quantum computing. Secondly, we obtain a sufficient condition for the existence of controllable subspaces of open quantum systems. In the context of control theory, we interpret why decoherence-free subspaces can be applied to quantum computing. Thirdly, we investigate the controllability of multiple-qubit systems when only single-qubit operations or two-qubit-interactive operations are permitted. It is demonstrated that only n(n + 3)/2 control Hamilton may guarantee open-loop controllability of n qubit systems in this case. Finally, we discuss the concept of generalized controllability of quantum systems. From the viewpoint of physical operations, we not only emphasize the limitation of open-loop controllability of quantum systems, but also clarify the rationality of redefining the concept of generalized controllability(3) Decoherence controlFirstly, we analyze the robustness of the quantum coherence tracking control scheme proposed by Lidar D. A. and Schneider S. [Quantum Information and Computation, 2005, 5(4): 350-363]. Not only the theoretical analysis is given in detail, but simulation examples are also presented to quantitatively illustrate how the coherence tracking control is subject to the precision of the initial condition and model parameters. Secondly, we develop a new scheme to overcome phase damping decoherence by combining open loop coherent control with periodic projective measurement based on the analysis of various decoherence control methods. The "softened" control objective in our scheme is to keep the state of the controlled qubit near a reference pure state with a high probability for a sufficiently long time. Two sub-optimal control problems are given in the sense of trace distance and fidelity, respectively, and they are eventually reduced to the design of a period T. Finally, it is found that the ability of performing quantum generalized measurement on open quantum systems, combined with the ability of coherence control and conditions of decoherence-free subspace(DFS), allows us to suppress quantum decoherence.(4) Analysis of typical quantum systemsSingle-qubit systems and atom-cavity-interactive systems are analyzed. Firstly, we explore the impact of a priori information on the optimal success probabilities of unambiguously discriminating two quantum states, and demonstrates how a priori information of the discriminated states, incomplete or complete, can be utilized to improve the optimal success probabilities. This result poses an interesting question: what physical operations can compensate the lack of a priori information in quantum world, which deserves further investigations in the future. Secondly, we demonstrate that combining QGM with coherent control will enhance the ability of controlling open quantum systems, and a qubit subject to dephasing decoherence is controllable via quantum generalized measurement. Thirdly, under the Rotation Wave Approximation condition, we reveal the evolution laws of an N-level atom interacting with (N - 1) mode cavity fields, and obtain the analytic solution of the corresponding schr(o|¨)dinger equation in the interaction picture. Finally, we demonstrate that the evolution of two non-identical two-level atoms simultaneously interacting with two-mode cavity fields can be reduced to the solution of linear time-invariant equations when the exact multiple-phonon resonance condition is satisfied. Furthermore, we examine the entanglement dynamics of two non-identical two-level atoms interacting with two-mode cavity fields. The thesis concludes with a summary of achievements and suggestions for future work to further expand our results.