Localizable entanglement

Popp, Markus; Verstraete, Frank; Martín-Delgado, M. A.; Cirac, J. I.

doi:10.1103/physreva.71.042306

Cited by 234 publications

(297 citation statements)

References 61 publications

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“…3 the behavior of this string order parameter S n for n = 1, 3, 5 is plotted. The existence of such a non-vanishing string order parameter can be traced back to the presence of diverging localizable entanglement [34,35]. This signals the presence of a symmetry protected topological order.…”

Section: The Order Parametersmentioning

confidence: 99%

Topological and nematic ordered phases in many-body cluster-Ising models

Giampaolo

Hiesmayr

2015

Phys. Rev. A

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We present a fully analytically solvable family of models with many-body cluster interaction and Ising interaction. This family exhibits two phases, dubbed cluster and Ising phases, respectively. The critical point turns out to be independent of the cluster size n + 2 and is reached exactly when both interactions are equally weighted. For even n we prove that the cluster phase corresponds to a nematic ordered phase and in the case of odd n to a symmetry protected topological ordered phase. Though complex, we are able to quantify the multiparticle entanglement content of neighboring spins. We prove that there exists no bipartite or, in more detail, no n + 1-partite entanglement. This is possible since the non-trivial symmetries of the Hamiltonian restrict the state space. Indeed, only if the Ising interaction is strong enough (local) genuine n + 2-partite entanglement is built up. Due to their analytically solvableness the n-cluster-Ising models serve as a prototype for studying non trivial-spin orderings and due to their peculiar entanglement properties they serve as a potential reference system for the performance of quantum information tasks.

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Section: The Order Parametersmentioning

confidence: 99%

Topological and nematic ordered phases in many-body cluster-Ising models

Giampaolo

Hiesmayr

2015

Phys. Rev. A

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“…The aim of this program of research is to shed new light on systems, particularly strongly correlated systems, that are difficult to treat with conventional approaches. Most studies have focused on quantum spin systems, especially near quantum phase transitions, see for example [1,2,3,4,5,6] and references therein. The concept of entanglement is well-defined in these systems as the spins can be considered distinguishable.…”

Section: Introductionmentioning

confidence: 99%

Entanglement of indistinguishable particles in condensed-matter physics

2006

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The concept of entanglement in systems where the particles are indistinguishable has been the subject of much recent interest and controversy. In this paper we study the notion of entanglement of particles introduced by Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] in several specific physical systems, including some that occur in condensed matter physics. The entanglement of particles is relevant when the identical particles are itinerant and so not distinguished by their position as in spin models. We show that entanglement of particles can behave differently to other approaches that have been used previously, such as entanglement of modes (occupation-number entanglement) and the entanglement in the two-spin reduced density matrix. We argue that the entanglement of particles is what could actually be measured in most experimental scenarios and thus its physical significance is clear. This suggests entanglement of particles may be useful in connecting theoretical and experimental studies of entanglement in condensed matter systems.

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“…We call this probability the singlet conversion probability (SCP). This, or other related quantities such as the localizable entanglement 15,16 , can be used as a figure of merit to characterize the state ρ and therefore the performance of the quantum network. Here, we focus on the SCP because of its operational meaning.…”

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confidence: 99%

Entanglement percolation in quantum networks

2007

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Quantum networks are composed of nodes that can send and receive quantum states by exchanging photons 1 . Their goal is to facilitate quantum communication between any nodes, something that can be used to send secret messages in a secure way 2,3 , and to communicate more efficiently than in classical networks 4 . These goals can be achieved, for instance, via teleportation 5 . Here we show that the design of efficient quantum-communication protocols in quantum networks involves intriguing quantum phenomena, depending both on the way the nodes are connected and on the entanglement between them. These phenomena can be used to design protocols that overcome the exponential decrease of signals with the number of nodes. We relate the problem of establishing maximally entangled states between nodes to classical percolation in statistical mechanics 6 , and demonstrate that phase transitions 7 can be used to optimize the operation of quantum networks.Quantum networks [8][9][10][11][12][13][14] , where different nodes are entangled, leading to quantum correlations that can be exploited by making local measurements at each node, will be the basis for the future of quantum communication. For instance, a set of quantum repeaters 10 can be considered as a simple quantum network where the goal is to establish quantum communication over long distances. To optimize the operation of such a network, it is required to establish efficient protocols of measurements in such a way that the probability of success in obtaining maximally entangled states between different nodes is maximized. This probability may behave very differently as a function of the number of nodes if we use different protocols: in some cases it may decay exponentially, something that makes the repeaters useless, whereas for some protocols it may decay only polynomially, something that would make them very efficient.A general network may be characterized by a quantum state, ρ, shared by the different nodes. The goal is then, given two nodes A and B, to find the measurements to be made at the nodes, assisted with classical communication, such that A and B share a maximally entangled state, or singlet, with maximal probability. We call this probability the singlet conversion probability (SCP). This, or other related quantities such as the localizable entanglement 15,16 , can be used as a figure of merit to characterize the state ρ and therefore the performance of the quantum network. Here, we focus on the SCP because of its operational meaning. These quantities cannot be determined in general, given that they require the optimization over all possible measurements in the different nodes, which is a formidable task even for small networks. consists of an arbitrary number of nodes in a given geometry sharing some quantum correlations, given by a global state ρ. b, Here we consider a simplified network where the nodes are disposed according to a well-defined geometry, for example the two-dimensional square lattice shown here, where each pair of nodes is connected by th...

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Localizable entanglement

Cited by 234 publications

References 61 publications

Topological and nematic ordered phases in many-body cluster-Ising models

Topological and nematic ordered phases in many-body cluster-Ising models

Entanglement of indistinguishable particles in condensed-matter physics

Entanglement percolation in quantum networks

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