Entanglement distribution in pure-state quantum networks

Perseguers, Sébastien; Cirac, J. I.; Acín, Antonio; Lewenstein, Maciej; Wehr, Jan

doi:10.1103/physreva.77.022308

Cited by 90 publications

(196 citation statements)

References 32 publications

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“…Any pure state can be put into this form via local unitary operations and α can be considered as a measure of the state's entanglement. Apart from basic entanglement percolation other techniques have also been proposed in pure state networks with smaller initial entanglement requirements [11][12][13]15]. These include the global error correction on a square network with no missing edges, as discussed in [21], and it was shown that a lower amount of entanglement was required to succeed at the expense of the final states' fidelity.…”

Section: Tradeoffs Between Different Strategies On Pure State Netmentioning

confidence: 99%

“…When this probability exceeds a geometry dependent threshold an infinite cluster is formed of linked nodes. Any two nodes in the cluster can then be transformed into a singlet using the process of entanglement swapping [12,18]. A singlet is generated between nodes with a probability that is independent of their separation.…”

Section: Introductionmentioning

confidence: 99%

“…By creating protocols for these higher dimensional networks the required amount of initial entanglement between the nodes can be reduced. This was first discussed for pure state networks and involved the use of 'entanglement percolation' [11][12][13][14][15][16]. The procedure uses the 'procrustean method' to transform each pure state into a maximally entangled singlet with a finite probability [17].…”

Section: Introductionmentioning

confidence: 99%

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Long-distance entanglement generation in two-dimensional networks

Dorner

Jaksch

2010

Phys. Rev. A

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We consider 2D networks composed of nodes initially linked by two-qubit mixed states. In these networks we develop a global error correction scheme that can generate distance-independent entanglement from arbitrary network geometries using rank two states. By using this method and combining it with the concept of percolation we also show that the generation of long distance entanglement is possible with rank three states. Entanglement percolation and global error correction have different advantages depending on the given situation. To reveal the trade-off between them we consider their application on networks containing pure states. In doing so we find a range of pure-state schemes, each of which has applications in particular circumstances: For instance, we can identify a protocol for creating perfect entanglement between two distant nodes. However, this protocol can not generate a singlet between any two nodes. On the other hand, we can also construct schemes for creating entanglement between any nodes, but the corresponding entanglement fidelity is lower.

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Section: Tradeoffs Between Different Strategies On Pure State Netmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Long-distance entanglement generation in two-dimensional networks

Dorner

Jaksch

2010

Phys. Rev. A

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“…These networks are based on the laws of quantum physics and will offer us new opportunities and phenomena as compared to their classical counterpart. Recently it has been shown that quantum phase transitions may occur in the entanglement properties of quantum networks defined on regular lattices, and that the use of joint strategies may be beneficial, for example, for quantum teleportation between nodes [9,10]. In this work we introduce a simple model of complex quantum networks, a new class of systems that exhibit some totally unexpected properties.…”

mentioning

confidence: 99%

Quantum random networks

Perseguers¹,

Lewenstein²,

Acín³

et al. 2010

Nature Phys

131

146

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In recent years, new algorithms and cryptographic protocols based on the laws of quantum physics have been designed to outperform classical communication and computation. We show that the quantum world also opens up new perspectives in the field of complex networks. Already the simplest model of a classical random network changes dramatically when extended to the quantum case, as we obtain a completely distinct behavior of the critical probabilities at which different subgraphs appear. In particular, in a network of N nodes, any quantum subgraph can be generated by local operations and classical communication if the entanglement between pairs of nodes scales as N −2 .On the one hand, complex networks describe a wide variety of systems in nature and society, as chemical reactions in a cell, the spreading of diseases in populations or communications using the Internet [1]. Their study has traditionally been the territory of graph theory, which initially focused on regular graphs, and was extended to random graphs by the mathematicians Paul Erdős and Alfréd Rényi in a series of seminal papers [2,3,4] in the 1950s and 1960s. With the improvement of computing power and the emergence of large databases, these theoretical models have become increasingly important, and in the past few years new properties which seem universal in real networks have been described, as a small-world [5] or a scale-free [6] behavior.On the other hand, quantum networks are expected to be developed in a near future in order to achieve, for instance, perfectly secure communications [7,8]. These networks are based on the laws of quantum physics and will offer us new opportunities and phenomena as compared to their classical counterpart. Recently it has been shown that quantum phase transitions may occur in the entanglement properties of quantum networks defined on regular lattices, and that the use of joint strategies may be beneficial, for example, for quantum teleportation between nodes [9,10]. In this work we introduce a simple model of complex quantum networks, a new class of systems that exhibit some totally unexpected properties. In fact we obtain a completely different classification of their behavior as compared to what one would expect from their classical counterpart.A classical network is mathematically represented by a graph, which is a pair of sets G = (V, E) where V is a set of N nodes (or vertices) and E is a set of L edges (or links) connecting two nodes. The theory of random graphs, aiming to tackle networks with a complex topology, considers graphs in which each pair of nodes i and j are joined by a link with probability p i,j . The simplest and most studied model is the one where this probability is independent of the nodes, with p i,j = p, and the resulting graph is denoted G N,p . The construction of these graphs can be considered as an evolution process:Evolution process of a classical random graph with N = 10 nodes: starting from isolated nodes, we randomly add edges with increasing probability p, to eventually get the co...

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“…Particularly, different nodes in a quantum network are usually connected by multipartite entangled states [3,4], and the twoparty quantum communication protocols between any two possible parities are not set in advance. For accomplishing two-party quantum communications, they need to previously establish bipartite entanglement between them via the help of other parties [5]. It is hence interesting to search efficient ways to extract entangled states with fewer particles (e.g., two particles) from multiparticle entangled states.…”

Section: Introductionmentioning

confidence: 99%

Manipulation of tripartite-to-bipartite entanglement localization under quantum noises and its application to entanglement distribution

Wang¹,

Tang²,

Yuan³

et al. 2014

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

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This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localization, and that the optimal strategy for reducing a three-qubit GHZ state to a two-qubit one via local measurements and classical communications in the amplitude-damping case is different from that in the noise-free case. We also show that the idea of entanglement localization could be utilized to improve the quality of bipartite entanglement distributing through amplitude-damping channels. These findings might shed a new light on entanglement manipulations and transformations.

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Entanglement distribution in pure-state quantum networks

Cited by 90 publications

References 32 publications

Long-distance entanglement generation in two-dimensional networks

Long-distance entanglement generation in two-dimensional networks

Quantum random networks

Manipulation of tripartite-to-bipartite entanglement localization under quantum noises and its application to entanglement distribution

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