Information sharing in quantum complex networks

Cardillo, Alessio; Galve, Fernando; Zueco, David; Gómez‐Gardeñes, Jesús

doi:10.1103/physreva.87.052312

Cited by 19 publications

(27 citation statements)

References 43 publications

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“…This has been possible because for these harmonic systems we have been able to calculate analytically not only the one-body reduced matrix for bosons and fermions, but also the von Neumann entropy in the bosonic case as well as the linear entropy in the fermionic case. In doing so, we complement and extend to harmonic systems with an arbitrary number of particles the study of entanglement recently done for various two-electron models [13,[21][22][23][24][25] as well as some helium-like systems [6,14,15,17] and certain quantum complex networks [49].…”

Section: Discussionmentioning

confidence: 99%

Entanglement in N-harmonium: bosons and fermions

Benavides-Riveros¹,

Toranzo²,

Dehesa³

2014

J. Phys. B: At. Mol. Opt. Phys.

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The ground-state entanglement of a single particle of the N-harmonium system (i.e., a completely-integrable model of N particles where both the confinement and the two-particle interaction are harmonic) is shown to be analytically determined in terms of N and the relative interaction strength. For bosons, we compute the von Neumann entropy of the one-body reduced density matrix by using the corresponding natural occupation numbers. There exists a critical number N c of particles so that below it, for positive values of the coupling constant, the entanglement grows when the number of particles is increasing; the opposite occurs for N > N c . For fermions, we compute the one-body reduced density matrix for the closed-shell spinned case. In the strong coupling regime, the linear entropy of the system decreases when N is growing. For fixed N , the entanglement is found (a) to decrease (increase) for negatively (positively) increasing values of the coupling constant, and (b) to grow when the energy is increasing. Moreover, the spatial and spin contributions to the total entanglement are found to be of comparable size.

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Section: Discussionmentioning

confidence: 99%

Entanglement in N-harmonium: bosons and fermions

Benavides-Riveros¹,

Toranzo²,

Dehesa³

2014

J. Phys. B: At. Mol. Opt. Phys.

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“…Then we multiply the above equation from the left side in e T κ and use the equations (4-21) and (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) to prove that…”

Section: Calculating Bipartite Entanglement In Stratificatin Basis Ofmentioning

confidence: 99%

“…And the entanglement entropy can be obtained from equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19).…”

Section: Examples:some Important Kinds Of Srgs Which Contain Nonisomomentioning

confidence: 99%

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Investigation graph isomorphism problem via entanglement entropy in strongly regular graphs

Jafarizadeh¹,

Eghbalifam²,

Nami³

2015

J. Stat. Mech.

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We investigate the quantum networks that their nodes are considered as quantum harmonic oscillators. The entanglement of the ground state can be used to quantify the amount of information one part of a network shares with the other part of the system.The networks which we studied in this paper, are called strongly regular graphs (SRG).These kinds of graphs have some special properties like they have three strata in the stratification basis. The Schur complement method is used to calculate the Schmidt number and entanglement entropy between two parts of graph. We could obtain analytically, all blocks of adjacency matrix in several important kinds of strongly regular graphs. Also * E-mail:jafarizadeh@tabrizu.ac.ir † E-mail:F.Egbali@tabrizu.ac.ir ‡ E-mail:S.Nami@tabrizu.ac.ir 1 Entanglement entropy 2 the entanglement entropy in the large coupling limit is considered in these graphs and the relationship between Entanglement entropy and the ratio of size of boundary to size of the system is found. Then, area-law is studied to show that there are no entanglement entropy for the highest size of system. Then, the graph isomorphism problem is considered in SRGs by using the elements of blocks of adjacency matrices. Two SRGs with the same parameters:(n, κ, λ, ν) are isomorphic if they can be made identical by relabeling their vertices. So the adjacency matrices of two isomorphic SRGs become identical by replacing of rows and columns.The nonisomirph SRGs could be distinguished by using the elements of blocks of adjacency matrices in the stratification basis, numerically.

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“…Moreover, the system allows to simulate quantum dynamics within the network by mapping the dynamical results of [34] for optimized experimental parameters of the optical multimode set-up. It is also important to note that each node of the network can be individually addressed which opens significant possibilities to probe the global properties of the network by detecting the local properties, as proposed in [34,41]. The proposal also opens the possibility to design quantum simulators for continuous variable open quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Reconfigurable optical implementation of quantum complex networks

et al. 2018

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Network theory has played a dominant role in understanding the structure of complex systems and their dynamics. Recently, quantum complex networks, i.e.collections of quantum systems arranged in a non-regular topology, have been theoretically explored leading to significant progress in a multitude of diverse contexts including, e.g., quantum transport, open quantum systems, quantum communication, extreme violation of local realism, and quantum gravity theories. Despite important progress in several quantum platforms, the implementation of complex networks with arbitrary topology in quantum experiments is still a demanding task, especially if we require both a significant size of the network and the capability of generating arbitrary topology-from regular to any kind of non-trivial structure-in a single setup. Here we propose an all optical and reconfigurable implementation of quantum complex networks. The experimental proposal is based on optical frequency combs, parametric processes, pulse shaping and multimode measurements allowing the arbitrary control of the number of the nodes (optical modes) and topology of the links (interactions between the modes) within the network. Moreover, we also show how to simulate quantum dynamics within the network combined with the ability to address its individual nodes. To demonstrate the versatility of these features, we discuss the implementation of two recently proposed probing techniques for quantum complex networks and structured environments.

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Information sharing in quantum complex networks

Cited by 19 publications

References 43 publications

Entanglement in N-harmonium: bosons and fermions

Entanglement in N-harmonium: bosons and fermions

Investigation graph isomorphism problem via entanglement entropy in strongly regular graphs

Reconfigurable optical implementation of quantum complex networks

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