Study On The Robustness Of Entanglement In Open Quantum Systems

Quantum information and quantum computation is an important area in the scientific research at present and the rising interdisciplinary field procreated through the combination of quantum theory with classical information science.Quantum entanglement is an indispensable physical resource in realizing quantum information and quantum computing.It denotes a strong relation between two or more quantum subsystems which is nonlocal and nonclassical,and it is also an essential feature that distinguishes quantum mechanics from classical mechanics.Entanglement is nowadays known to be at the heart of many potential applications,such as Quantum computation,quantum secure direct communication,quantum teleportation,quantum dense coding,quantum key distribution and so on.However,there is no absolutely closed system,a real quantum system inevitably interacts with its surrounding environment,which leads to decoherence phenomena.The decoherence can destroy the initial entanglement in the quantum system which is the crucial resource in the quantum information processing tasks.Therefore,it is necessary to study the decoherence of entanglement in realistic environments.A well known decoherence phenomenon in two qubit system is entanglement sudden death,entanglement decreasing to zero abruptly,under the influence of local environment.The experimental evidences of this interesting phenomenon have been observed in a two-qubit optical system.In recent years,more and more scientists are interested in the study of entanglement robustness under various decoherence models,and great progress has been made in this field.The investigation on quantum entanglement evolution and robustness of open systems can promote the development of many branches of quantum information,including the construction of quantum gates,the evolution speed of quantum systems,quantum state fidelity and quantum communication efficiency.The study of entanglement robustness of open quantum systems is not only helpful for people to have a deeper understanding of quantum entanglement,but also helpful for people to make better use of quantum information technology.This paper introduces the robustness of entanglement during decoherence in the open systems and obtain some interesting results.The main content of this paper is described as follows:First,the exploration on the entanglement dynamics of bipartite systems is the premise to understand the evolution of entanglement,since they are the most basic entanglement systems.This paper,through the analytical and numerical methods,the robustness of entanglement of a qubit-qudit system(qudit system has d levels with d ? 3)under depolarizing and dephasing channel is investigated systematically.For depolarizing channel,the decoherence process of entanglement for arbitrary qubit-qudit systems is obtained.The robustness of an arbitrary qubit-qudit pure state with the same initial entanglement increases with the dimension of qudit subsystem d.For dephasing channel,the most robust entangled states and the most fragile ones are found for the qubit-qudit system(qudit in the special case d =3,4,(43),12)during the decoherence.Furthermore,the dephasing process of these qubit-qudit states is independent of the dimension d.Second,it is very important to study the decoherence of multiparty entanglement for it has more abundant properties.The robustness of three-qubit states under three different decoherence channels(amplitude damping,dephasing,bit flip)systematically are investigated,and the most robust genuine tripartite entangled states and the most fragile ones during each of the three decoherence processes are found.Moreover,the states with the most significant difference in robustness are shown to be locally unitarily equivalent to each other and therefore possess precisely the same entanglement properties.The results of this paper show that the local unitary operation can greatly enhance the robustness of entanglement of a three-qubit state in some special realistic environments.Third,large-scale entanglement is an important resource in quantum information processing.The entanglement robustness of n-qubit(n =2,4,5,6,and 7)states under dephasing and bit flip channel is studied,and the most robust genuine n-qubit entangled states and the most fragile ones are found during the decoherence process.The most robust and fragile states are equivalent under a local unitary operations,and therefore possess precisely the same entanglement properties.It confirms that,for dephasing and bit flip channel,the local unitary operation can greatly enhance the robustness of entanglement of n-qubit states.