Semidefinite Tests for Quantum Network Topologies

Åberg, Johan; Nery, Ranieri; Duarte, Cristhiano; Chaves, Rafael

doi:10.1103/physrevlett.125.110505

Cited by 59 publications

(60 citation statements)

References 41 publications

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“…Using these techniques as well as concepts based on covariance matrices 28 , 29 and classical networks 23 , one can also derive bounds on the maximal GHZ fidelity achievable by network states. In fact, for network states holds, as explained in Supplementary Note 2 .…”

Section: Resultsmentioning

confidence: 99%

“…First, the problem has been considered in the classical setting, such as the analysis of causal structures 15 – 17 or in the study of hidden variable models, where the hidden variables are not equally distributed between every party 18 – 24 . Concerning quantum correlations, several initial works appeared in the last year, suggesting slightly different definitions of network entanglement 25 – 28 . These have been further investigated 29 – 31 and methods from the classical realm have been extended to the quantum scenario 32 .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques

Hansenne

Kraft

et al. 2022

Nat Commun

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Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that entangled quantum states with a bosonic or fermionic symmetry can not be generated in networks; moreover, cluster and graph states are not accessible. Our methods can be used to design certification methods for the functionality of specific links in a network and have implications for the design of future network structures.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques

Hansenne

Kraft

et al. 2022

Nat Commun

View full text Add to dashboard Cite

show abstract

“…Using these techniques as well as concepts based on covariance matrices [28,29] and classical networks [23], one can also derive bounds on the maximal GHZ fidelity achievable by network states. In fact, for network states…”

Section: Networkmentioning

confidence: 99%

“…First, the problem has been considered in the classical setting, such as the analysis of causal structures [15][16][17] or in the study of hidden variable models, where the hidden variables are not equally distributed between every party [18][19][20][21][22][23][24]. Concerning quantum correlations, several initial works appeared in the last year, suggesting slightly different definitions of network entanglement [25][26][27][28]. These have been further investigated [29][30][31] and methods from the classical realm have been extended to the quantum scenario [32].…”

Section: Introductionmentioning

confidence: 99%

Quantum Networks and Symmetries

Hansenne¹,

Kraft³

et al. 2021

Preprint

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“…The key idea is to consider the various sources in the network to be statistically independent [7][8][9]. This independence leads to nonconvexity in the space of relevant correlations, undermining the use of preexisting tools and creating a need for new approaches, both analytically [10][11][12][13][14][15][16][17][18] and numerically [19]. The network structure offers new interesting effects, such as the possibility to certify quantum nonlocality "without inputs" (i.e., a scenario where each party performs a fixed quantum measurement) [8,9,[20][21][22].…”

mentioning

confidence: 99%

Network Quantum Steering

et al. 2021

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The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show how the results from Bell nonlocality and quantum steering can be used to demonstrate network steering. We further show that it is a genuinely novel effect by exhibiting unsteerable states that nevertheless demonstrate network steering based upon entanglement swapping yielding a form of activation. On the other hand, we provide no-go results for network steering in a large class of scenarios by explicitly constructing NLHS models.

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Semidefinite Tests for Quantum Network Topologies

Cited by 59 publications

References 41 publications

Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques

Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques

Quantum Networks and Symmetries

Network Quantum Steering

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