Long-range quantum entanglement in noisy cluster states

Raussendorf, Robert; Bravyi, Sergey; Harrington, Jim

doi:10.1103/physreva.71.062313

Cited by 167 publications

(259 citation statements)

References 20 publications

Supporting

Mentioning

254

Contrasting

Order By: Relevance

“…As we perturb away from this point, if the correlation length ξ also increases then newer degrees of freedom get involved in the entanglement spectrum as a result of which the lower (α → 0) entropies increase, on the other hand the higher α entropies decrease because of the algebraic suppression of the contributions from the new small but non-zero values in the spectrum and loss of contributions from the previously non-zero larger eigenvalues. We comment that since similar phenomenology in the entanglement spectrum is known to be displayed in cluster states [64,65,92], or more generally in all graph states [66], similar findings in the Rényi entropies response should apply to those as well. Our work here should be seen as supporting a growing body of evidence [24,38] that this characteristic perturbative response would hold for a wider class of states such as quantum double models, cluster states and other quantum spin liquids.…”

Section: Discussionmentioning

confidence: 93%

“…Further, that it is a necessary but not sufficient condition exhibited by such states. A case in point is the analysis for cluster states [64,65,92] shown in Fig. (11).…”

Section: Discussionmentioning

confidence: 99%

“…Cluster states do not possess topological order even though they permit no local order parameter [64,65,92]. A numerical analysis of their local convertibility properties as shown in Fig.…”

Section: Appendix C: Behavior Of Rényi Entropies For the Cluster Statementioning

confidence: 99%

See 2 more Smart Citations

Local convertibility of the ground state of the perturbed toric code

et al. 2014

View full text Add to dashboard Cite

We present analytical and numerical studies of the behaviour of the α-Renyi entropies in the Toric code in presence of several types of perturbations aimed at studying the simulability of these perturbations to the parent Hamiltonian using local operations and classical communications (LOCC) -a property called localconvertibility. In particular, the derivatives, with respect to the perturbation parameter, present different signs for different values of α within the topological phase. From the information-theoretic point of view, this means that such ground states cannot be continuously deformed within the topological phase by means of catalyst assisted local operations and classical communications (LOCC). Such LOCC differential convertibility is on the other hand always possible in the trivial disordered phase. The non-LOCC convertibility is remarkable because it can be computed on a system whose size is independent of correlation length. This method can therefore constitute an experimentally feasible witness of topological order.

show abstract

Section: Discussionmentioning

confidence: 93%

“…Further, that it is a necessary but not sufficient condition exhibited by such states. A case in point is the analysis for cluster states [64,65,92] shown in Fig. (11).…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Local convertibility of the ground state of the perturbed toric code

et al. 2014

View full text Add to dashboard Cite

show abstract

“…In this picture a finite temperature phase transition for LE could possibly occur for two or more dimensions. We note that recently such a transition has been shown to exist for 3D cluster states [14]. Finally we would like to point out that, although the entanglement length of the AKLT model is finite for T > 0, it can still be considerably large for sufficiently low temperatures T < ∼ 0.2.…”

Section: B Example: Aklt Modelmentioning

confidence: 99%

Localizable entanglement

Popp¹,

Verstraete²,

et al. 2005

View full text Add to dashboard Cite

We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of Localizable Entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.

show abstract

“…However, these proposals are challenging to extend to higher order many-body interactions as these terms arise within a perturbation series and thus become exponentially weaker the more particles participate in the interaction [6,7]. On the other hand, such spin models with many-body interactions have recently received great attention in the context of Kitaev's toric code Hamiltonian [15], which has interesting topological properties, and for the generation of cluster states, which are relevant for measurement-based quantum computing [16].…”

Section: Introductionmentioning

confidence: 99%

Quantum simulation of many-body spin interactions with ultracold polar molecules

Weimer

2013

Molecular Physics

View full text Add to dashboard Cite

We present an architecture for the quantum simulation of many-body spin interactions based on ultracold polar molecules trapped in optical lattices. Our approach employs digital quantum simulation, i.e., the dynamics of the simulated system is reproduced by the quantum simulator in a stroboscopic pattern, and allows to simulate both coherent and dissipative dynamics. We discuss the realization of Kitaev's toric code Hamiltonian, a paradigmatic model involving fourbody interactions, and we analyze the requirements for an experimental implementation.

show abstract

Long-range quantum entanglement in noisy cluster states

Cited by 167 publications

References 20 publications

Local convertibility of the ground state of the perturbed toric code

Local convertibility of the ground state of the perturbed toric code

Localizable entanglement

Quantum simulation of many-body spin interactions with ultracold polar molecules

Contact Info

Product

Resources

About