Fidelity threshold for long-range entanglement in quantum networks

Perseguers, Sébastien

doi:10.1103/physreva.81.012310

Cited by 24 publications

(39 citation statements)

References 23 publications

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“…Here we have complemented it with a simple scheme of encoding/decoding an unknown state, which allows to obtain node-to-node entanglement percolation. Our scheme, similarly to that of [21], needs three dimensions. Two of them scale only logarithmically with the third one -the distance between the nodes which want to share entanglement.…”

Section: Implications For Entanglement Percolationmentioning

confidence: 99%

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Long-distance quantum communication over noisy networks without long-time quantum memory

et al. 2014

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The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension D and transmission of quantum information in a D + 1-dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) network, even when taking into account that encoding and decoding of a state is exposed to an error. For 3D networks we propose a simple encoding and decoding scheme based solely on syndrome measurements on 2D Kitaev topological quantum memory. Our procedure constitutes an alternative scheme of state injection that can be used for universal quantum computation on 2D Kitaev code. It is shown that the encoding scheme is equivalent to teleporting the state, from a specific node into a whole two-dimensional network, through some virtual EPR pair existing within the rest of network qubits. We present an analytic lower bound on fidelity of the encoding and decoding procedure, using as our main tool a modified metric on space-time lattice, deviating from a taxicab metric at the first and the last time slices.Suppose we have a network of laboratories with some fixed distance between neighboring ones, and one of them wants to establish quantum communication with another one. We assume that neighboring labs can directly exchange quantum communication with some small, fixed error. This can be used e.g. to share some noisy Einstein-Podolsky-Rosen (EPR) pairs between the neighboring labs. We also assume that all operations performed within each lab may be faulty with some fixed, small probability. If two distant labs can achieve quantum communication with the help of all the labs in the network, then they can exploit it to share cryptographic key that will be known only to these two labs. This scenario was put forward in [1], and is an alternative to quantum repeaters [2,3]. It is also closely related to entanglement percolation [4]. In [1] the question was posed whether for a 2-dimensional network, in principle, one can perform quantum communication over an arbitrary distance, provided that one can execute gates between the adjacent nodes (i.e. local gates), and the size of the system in each node is constant (i.e. it does not depend on the distance), so that the nodes do not need quantum memory. The answer was affirmative. Namely, the authors represented nearest neighbour quantum computation on a line as a teleportation process on quantum 2-dimensional square networks, where entangled pairs are shared between adjacent nodes (i.e. between those that are separated by a size of an elementary cell a of the network). 1-dimensional system for quantum computation is formed by all nodes belonging to a chosen line forming a diagonal of elementary ce...

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Section: Implications For Entanglement Percolationmentioning

confidence: 99%

“…Indeed, we do not need to perform the flips in the encoding scheme: it is enough to store this information classically. Communication scheme of [21] uses correlations between the nodes emerging from their initial preparation in a cluster state, whereas our method relies on EPR pairs shared by adjacent nodes.…”

Section: Implications For Entanglement Percolationmentioning

confidence: 99%

Long-distance quantum communication over noisy networks without long-time quantum memory

et al. 2014

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“…[21], requires states of rank two, or less, for long distance entanglement generation using constant resources. So far no protocol has been able to transform a 2D network of full rank states into a highly entangled two qubit state with no dependence on the qubit separation, although this is possible in infinite 3D networks [22].…”

Section: Introductionmentioning

confidence: 99%

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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“…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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Fidelity threshold for long-range entanglement in quantum networks

Cited by 24 publications

References 23 publications

Long-distance quantum communication over noisy networks without long-time quantum memory

Long-distance quantum communication over noisy networks without long-time quantum memory

Long-distance entanglement generation in two-dimensional networks

Thermodynamic formalism for dissipative quantum walks

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