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Quantum repeaters based on CNOT gate under decoherence
TONG Zhao-yang, LIAO Ping, KUANG Le-man
Front. Phys. . 2007, 2 (4): 389-402.
https://doi.org/10.1007/s11467-007-0061-0
In this paper, we study single-qubit and single-user quantum repeaters based on CNOT gates under decoherence using the Kraus-operator representations of decoherence. We investigate the influence of decoherence on the information-disturbance trade-off of quantum repeaters. It is found that decoherence may lead to the appearance of three subspaces, called as the normal subspace, the anomalous subspace, and the decoherence-free subspace (DFS), respectively. It is indicated that in the normal subspace decoherence decreases the transmission and estimation fidelities, in the anomalous subspace decoherence enhances these fidelities, and in the DFS these fidelities do not change. The concept of the quality factor is introduced to evaluate the quality of the quantum repeater. It is indicated that the quality factor can be efficiently controlled and manipulated by changing the initial state of the probe qubit. It is found that under certain conditions the quantum repeater can be optimal even in the presence of decoherence.
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Synchronization in complex clustered networks
HUANG Liang, Kwangho PARK, LAI Ying-Cheng, WANG Xingang, LAI Choy Heng, Robert A. GATENBY
Front. Phys. . 2007, 2 (4): 446-459.
https://doi.org/10.1007/s11467-007-0056-x
Synchronization in complex networks has been an active area of research in recent years. While much effort has been devoted to networks with the small-world and scale-free topology, structurally they are often assumed to have a single, densely connected component. Recently it has also become apparent that many networks in social, biological, and technological systems are clustered, as characterized by a number (or a hierarchy) of sparsely linked clusters, each with dense and complex internal connections. Synchronization is fundamental to the dynamics and functions of complex clustered networks, but this problem has just begun to be addressed. This paper reviews some progress in this direction by focusing on the interplay between the clustered topology and network synchronizability. In particular, there are two parameters characterizing a clustered network: the intra-cluster and the inter-cluster link density. Our goal is to clarify the roles of these parameters in shaping network synchronizability. By using theoretical analysis and direct numerical simulations of oscillator networks, it is demonstrated that clustered networks with random inter-cluster links are more synchronizable, and synchronization can be optimized when inter-cluster and intra-cluster links match. The latter result has one counterintuitive implication: more links, if placed improperly, can actually lead to destruction of synchronization, even though such links tend to decrease the average network distance. It is hoped that this review will help attract attention to the fundamental problem of clustered structures/synchronization in network science.
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Enhancing the network synchronizability
ZHAO Ming, ZHOU Tao, CHEN Guan-rong, WANG Bing-hong
Front. Phys. . 2007, 2 (4): 460-468.
https://doi.org/10.1007/s11467-007-0058-8
The structural and dynamical properties, particularly the small-world effect and scale-free feature, of complex networks have attracted tremendous interest and attention in recent years. This article offers a brief review of one focal issue concerning the structural and dynamical behaviors of complex network synchronization. In the presentation, the notions of synchronization of dynamical systems on networks, stability of dynamical networks, and relationships between network structure and synchronizability, will be first introduced. Then, various technical methods for enhancing the network synchronizability will be discussed, which are roughly divided into two classes: Structural Modification and Coupling-Pattern Regulation, where the former includes three typical methods—dividing hub nodes, shortening average distances, and deleting overload edges, while the latter mainly is a method of strengthening the hub-nodes’ influence on the network.
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11 articles
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