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**Name**:

# Theoretical Study of Quantum Information Pro-Cessing in Cavity QED and Spin Systems

**Author**: HuZhengDa

**Tutor**: XuJingBo

**School**: Zhejiang University

**Course**: Theoretical Physics

**Keywords**: quantum communication,quantum entanglement,quantum discord,in-formation flow,qua

**CLC**: O413.1

**Type**: PhD thesis

**Year**: 2013

Abstract:

Quantum information science is a new inter-discipline about the physics, math and com-puter science. It carries out information tasks based on the principles of quantum mechanics, which is entirely different from the classical information science following the rules of classical physics. Much work has been done in this completely new area and remarkable results have been achieved, such as quantum Turing machine, quantum teleportation and quantum cryptography. However, the quantum resource needed in these quantum tasks is very fragile and easily de-stroyed due to decoherence induced by the surrounding environment. The decoherence is a main obstacle to the practical application of quantum information processing and thus how to protect and control the quantum resource is of prime importance. Besides, the realization of scalable quantum networks is critical to quantum communication. In this thesis, we review our theoretical researches on quantum correlations and relevant issues. The main work is listed as follows:First, we investigate quantum communication in quantum networks of one dimensional fiber-coupled cavity arrays. The quantum network consists of a number of cavities each of which is doped with a two-level atom and adjacent cavities are connected by a fiber. Based on quantum networks of this type, we discuss several quantum tasks such as quantum state transfer, entan-gling and entanglement transfer. It is shown that high fidelity of state transfer can still be possible for certain states even the number of nodes has been large and almost perfect state transfer can be realized for some specific numbers of nodes. The properties of entanglement transfer through double parallel arrays and the influence of the initial target state parameters, the number of nodes of the two arrays and their difference in number on the entanglement dynamics are studied as well. Moreover, we generalize the one-atom case to the N-atom case and use the mean field approximation to explore the quantum phase transition in this many body system. The phase di-agrams are obtained for cases with different numbers of atoms in single cavity. Quantum phase transition is a pure quantum effect due to quantum fluctuation. We find that quantum phase tran-sition can occur near the critical points in this fiber-coupled cavity array. It is also shown that the fidelity and the entanglement entropy for the ground state can have the phenomena of sud-den reduction and sudden transition, respectively. Besides, to confirm this existence of phase transition, the photon population imbalance of adjacent cavities is analytically explored via the simplest configuration which consists of two cavities coupled by a fiber.Then, we study the issue of control of quantum information in cavity QED systems. Based on the trace distance, we investigate the control of information flow via the model of two non-interacting atoms coupled to a single cavity mode and the use of total correlation in the thermal state to detect the critical points at energy-level crossings. By applying projective measurements, we show that the information of the two-atom subsystem can be protected to its initial value by intensive measurements and be enhanced by a single measurement. In addition, we show that the information flow is closely related to entanglement and quantum discord and address the issue of how to utilize the total correlation of thermal state to detect the critical points at energy-level crossings. On the other hand, we investigate the manipulation of information flow as well as the quantum correlations via dissipative superconducting flux qubits. We identify that the information flow based on trace distance is equivalent to the quantum Fisher information flow in the resonant case. Moreover, we discuss the the effects of the time-dependent magnetic field and of partial-collapse quantum measurements on the information flow and the quantum correlations, respectively. By applying two partial-collapse quantum measurements, we can effectively store the quantum resource and obtain stable amount of quantum correlations. It is found that the effect of the time-dependent magnetic field depends largely on whether the system is in the Markovian or the non-Markvian regime. The combined action of time-dependent magnetic fields and partial-collapse quantum measurements can storage the quantum resource better.Another aspect of our work is the quantum information processing in spin systems. We investigate quantum communication in spin chains with three-site and DzyaloshinskyMoriya in-teractions. It is found that both the two extra interactions can improve the quality of quantum communication, however, with different effects. Via the transfer of quantum discord, we show that the three-site coupling may enhance the maximum discord transferred more obviously while the Dzyaloshinsky Moriya coupling may accelerate the maximum discord transferred more effec-tively. Besides, we also find that the behaviors of transfer of entanglement and quantum discord can differ greatly. We also study the evolution of quantum correlation via two independent qubits individually coupled to rings of thermal spin baths. It is found that the decay of quantum discord exhibit the phenomenon of sudden transition. We verify that critical points in quantum phase transition can be detected via the sudden transition in the decay of quantum discord. We also examine how to protect the quantum discord of the two-qubit system by applying a series of ¦Ð-phase pulses. In addition, we investigate the more practical situation for spin chains with open boundary conditions. The necessary conditions for the occurrence of sudden transition and sud-den change phenomena for the dynamics of quantum discord are derived. We demonstrate the sudden transition and sudden change phenomena via the models of two separate qubits coupled to two independent open spin environments and to a common open spin environment, respectively. Furthermore, the quantum criticality of the open spin environment is discussed by exploring the probability distribution of the Loschmidt echo and the scaling transformation behavior of quan-tum discord dynamics.

Quantum information science is a new inter-discipline about the physics, math and com-puter science. It carries out information tasks based on the principles of quantum mechanics, which is entirely different from the classical information science following the rules of classical physics. Much work has been done in this completely new area and remarkable results have been achieved, such as quantum Turing machine, quantum teleportation and quantum cryptography. However, the quantum resource needed in these quantum tasks is very fragile and easily de-stroyed due to decoherence induced by the surrounding environment. The decoherence is a main obstacle to the practical application of quantum information processing and thus how to protect and control the quantum resource is of prime importance. Besides, the realization of scalable quantum networks is critical to quantum communication. In this thesis, we review our theoretical researches on quantum correlations and relevant issues. The main work is listed as follows:First, we investigate quantum communication in quantum networks of one dimensional fiber-coupled cavity arrays. The quantum network consists of a number of cavities each of which is doped with a two-level atom and adjacent cavities are connected by a fiber. Based on quantum networks of this type, we discuss several quantum tasks such as quantum state transfer, entan-gling and entanglement transfer. It is shown that high fidelity of state transfer can still be possible for certain states even the number of nodes has been large and almost perfect state transfer can be realized for some specific numbers of nodes. The properties of entanglement transfer through double parallel arrays and the influence of the initial target state parameters, the number of nodes of the two arrays and their difference in number on the entanglement dynamics are studied as well. Moreover, we generalize the one-atom case to the N-atom case and use the mean field approximation to explore the quantum phase transition in this many body system. The phase di-agrams are obtained for cases with different numbers of atoms in single cavity. Quantum phase transition is a pure quantum effect due to quantum fluctuation. We find that quantum phase tran-sition can occur near the critical points in this fiber-coupled cavity array. It is also shown that the fidelity and the entanglement entropy for the ground state can have the phenomena of sud-den reduction and sudden transition, respectively. Besides, to confirm this existence of phase transition, the photon population imbalance of adjacent cavities is analytically explored via the simplest configuration which consists of two cavities coupled by a fiber.Then, we study the issue of control of quantum information in cavity QED systems. Based on the trace distance, we investigate the control of information flow via the model of two non-interacting atoms coupled to a single cavity mode and the use of total correlation in the thermal state to detect the critical points at energy-level crossings. By applying projective measurements, we show that the information of the two-atom subsystem can be protected to its initial value by intensive measurements and be enhanced by a single measurement. In addition, we show that the information flow is closely related to entanglement and quantum discord and address the issue of how to utilize the total correlation of thermal state to detect the critical points at energy-level crossings. On the other hand, we investigate the manipulation of information flow as well as the quantum correlations via dissipative superconducting flux qubits. We identify that the information flow based on trace distance is equivalent to the quantum Fisher information flow in the resonant case. Moreover, we discuss the the effects of the time-dependent magnetic field and of partial-collapse quantum measurements on the information flow and the quantum correlations, respectively. By applying two partial-collapse quantum measurements, we can effectively store the quantum resource and obtain stable amount of quantum correlations. It is found that the effect of the time-dependent magnetic field depends largely on whether the system is in the Markovian or the non-Markvian regime. The combined action of time-dependent magnetic fields and partial-collapse quantum measurements can storage the quantum resource better.Another aspect of our work is the quantum information processing in spin systems. We investigate quantum communication in spin chains with three-site and DzyaloshinskyMoriya in-teractions. It is found that both the two extra interactions can improve the quality of quantum communication, however, with different effects. Via the transfer of quantum discord, we show that the three-site coupling may enhance the maximum discord transferred more obviously while the Dzyaloshinsky Moriya coupling may accelerate the maximum discord transferred more effec-tively. Besides, we also find that the behaviors of transfer of entanglement and quantum discord can differ greatly. We also study the evolution of quantum correlation via two independent qubits individually coupled to rings of thermal spin baths. It is found that the decay of quantum discord exhibit the phenomenon of sudden transition. We verify that critical points in quantum phase transition can be detected via the sudden transition in the decay of quantum discord. We also examine how to protect the quantum discord of the two-qubit system by applying a series of ¦Ð-phase pulses. In addition, we investigate the more practical situation for spin chains with open boundary conditions. The necessary conditions for the occurrence of sudden transition and sud-den change phenomena for the dynamics of quantum discord are derived. We demonstrate the sudden transition and sudden change phenomena via the models of two separate qubits coupled to two independent open spin environments and to a common open spin environment, respectively. Furthermore, the quantum criticality of the open spin environment is discussed by exploring the probability distribution of the Loschmidt echo and the scaling transformation behavior of quan-tum discord dynamics.

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