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Quantum entanglement properties of three - qubit system

Author: WangYanHui
Tutor: XiaYunJie
School: Qufu Normal University
Course: Theoretical Physics
Keywords: thermal entanglement Dzyaloshinskii-Moriyanon interaction non-Markovian environment environment entanglement sudden death
CLC: O431.2
Type: Master's thesis
Year: 2010
Downloads: 78
Quote: 0
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Abstract


Quantum mechanical is the theory of non-localized, which has been confirmed by the experimental results contrary to Bell’s inequality. Therefore, quantum mechanics reveals a number of counter-intuitive effects. The state which can not be expressed as a direct product form in quantum mechanics is called entangled state. Historically, the concept of entangled states was first proposed by Schrodinger on the "cat state" of the paper in 1935.The so-called quantum entanglement refers to that non-classical strong correlation exists in two or more quantum system. Quantum entanglement has great significance in understanding the basic concepts of quantum mechanics, relating to reality, locality, hidden variable theories, measurement of basic issues and etc. in quantum mechanics. In recent years, quantum entanglement is regarded as an irreplaceable resource that can be used to perform some impossible task of classical instruments, such as quantum teleportation, quantum cryptography and etc. due to the production and development of quantum information and quantum computing.So in this thesis, we focus our research on the thermal entanglement in spin-system and the entanglement dynamics in environment' dissertation">non-Markovian environment.1. We study the improvement and manipulation of pairwise thermal entanglement in one-dimentional three-qubit Heisenberg model, where Dzyaloshinskii-Moriya (DM) interaction is considered and concurrence is calculated to research this entanglement property. The results show that for XXX model, DM interaction can induce entanglement in the antiferromagnetic and ferromagnetic spin chains although the required critical values are different for both cases. For XXZ model,by introducing DM interaction D, antiferromagnetic spin chain exists entanglement which is absent when D=0, and in addition, for antiferromagnetic and ferromagnetic case, DM interaction D and the anisotropy parameterΔhave different effects on entanglement. As a result, the entanglement can be controlled and enhanced by choosing appropriate DM interaction and anisotropy parameter. Furthermore, we find that at the same temperature, no matter for antiferromagnetic or ferromagnetic spin chains, the critical DM interaction inducing entanglement should be greater in a three-qubit XXZ model than that in a two-qubit XXZ model according to the comparison between them.2. We study the entanglement dynamics of three two-level atoms interacting with a structured reservoir. The atoms are initially prepared in a mixed W state while the reservoir in the vacuum. We show the dependence of entanglement dynamics on the purity of initial atomic state and on the amount of non-Markovianity. When the initial state of atoms is in a W pure state, the entanglement will decay asymptotically, while it vanishes in a finite time if the initial state is in a mixed W state. In addition, as the memory effect of the environment, entanglement can partially revive after it vanishes, and the revival degree is dependent on the strength of non-Markovian effect. In the end, we consider the entanglement generation and its evolution when the initial state of atoms system is completely separable.

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CLC: > Mathematical sciences and chemical > Physics > Optics > The light nature of the theory > Quantum optics
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