Entanglement percolation on a quantum internet with scale-free and clustering characters

Wu, Liang; Zhu, Shiqun

doi:10.1103/physreva.84.052304

Cited by 8 publications

(4 citation statements)

References 29 publications

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“…The synergy between the field of complex networks and that of information theory has recently appealed to the quantum information community [19,20]. As a product, classical results on percolation theory [21][22][23][24] and network science, such as the small-world effect [25], have been revisited in networked structures of coupled quantum systems as a first step for designing quantum communication networks. Conversely, the use of quantum dynamical processes, such as quantum random walks [26,27] and their application to rank the importance of network elements [28][29][30][31], has given new quantum information perspectives to classical problems of the network realm.…”

Section: Introductionmentioning

confidence: 99%

Information sharing in quantum complex networks

et al. 2013

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We introduce the use of entanglement entropy as a tool for studying the amount of information shared between the nodes of quantum complex networks. By considering the ground state of a network of coupled quantum harmonic oscillators, we compute the information that each node has on the rest of the system. We show that the nodes storing the largest amount of information are not the ones with the highest connectivity, but those with intermediate connectivity thus breaking down the usual hierarchical picture of classical networks. We show both numerically and analytically that the mutual information characterizes the network topology. As a byproduct, our results point out that the amount of information available for an external node connecting to a quantum network allows to determine the network topology.

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Section: Introductionmentioning

confidence: 99%

Information sharing in quantum complex networks

et al. 2013

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“…Since its first appearance in ref. 1, the concept of scale-free complex networks has broadened itself more rapidly than anyone expected, and its abundance in real life now arguably encompasses many areas from fundamental physics (8)(9)(10)(11) to social systems (12,13). Consequently, scale-free complex networks are now commonly regarded as an essential substrate for studying many other facets in network science (14)(15)(16)(17)(18)(19)(20)(21)(22)(23), such as percolation (24)(25)(26), epidemic spreading (27)(28)(29), and information diffusion (30)(31)(32)(33).…”

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confidence: 99%

Power-law distribution of degree–degree distance: A better representation of the scale-free property of complex networks

Zhou

Meng

Stanley

2020

Proc. Natl. Acad. Sci. U.S.A.

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Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset,Nat. Commun.10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree–degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree–degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree–degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree–degree distance distribution better represents the scale-free property of a complex network.

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“…We introduce two new quantum centrality measures [37], the activity rank and the stability rank. These measures are of relevance in the context of complex networks theory [38][39][40], providing another connection between complex networks and quantum information theory [35,[41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. Another interesting aspect of the thermodynamic approach to dissipative quantum walks is the possibility to frame dynamical phases of the evolution in the standard language of Statistical Mechanics and Thermodynamics.…”

Section: Discussionmentioning

confidence: 99%

Thermodynamic formalism for dissipative quantum walks

Garnerone

2012

Phys. Rev. A

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We consider the dynamical properties of dissipative continuous time quantum walks on directed graphs. Using a large deviation approach we construct a thermodynamic formalism allowing us to define a dynamical order parameter, and to identify transitions between dynamical regimes. For a particular class of dissipative quantum walks we propose a new quantum generalization of the the classical pagerank vector, used to rank the importance of nodes in a directed graph. We also provide an example where one can characterize the dynamical transition from an effective classical random walk to a dissipative quantum walk as a thermodynamic crossover between distinct dynamical regimes.

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Entanglement percolation on a quantum internet with scale-free and clustering characters

Cited by 8 publications

References 29 publications

Information sharing in quantum complex networks

Information sharing in quantum complex networks

Power-law distribution of degree–degree distance: A better representation of the scale-free property of complex networks

Thermodynamic formalism for dissipative quantum walks

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