Quantum Inflation: A General Approach to Quantum Causal Compatibility

Wolfe, Elie; Pozas-Kerstjens, Alejandro; Grinberg, Matan; Rosset, Denis; Acín, Antonio; Navascués, Miguel

doi:10.1103/physrevx.11.021043

Cited by 48 publications

(78 citation statements)

References 54 publications

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“…By considering increasingly large inflations, one obtains increasingly strong conditions for the correlations of interest. Concretely, inflation-based methods have been developed to characterize correlations in networks where all sources are local [37], quantum [38], and general nonlocal resources [37,39]. By combining the ideas from the first and last, one obtains a computationally viable and generally applicable tool to analyze correlations in networks that are composed of both local and general nonlocal resources.…”

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confidence: 99%

Full Network Nonlocality

2022

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Networks have advanced the study of nonlocality beyond Bell's theorem. Here, we introduce the concept of full network nonlocality, which describes correlations that necessitate all links in a network to distribute nonlocal resources. Showcasing that this notion is stronger than standard network nonlocality, we prove that the most well-known network Bell test does not witness full network nonlocality. In contrast, we demonstrate that its generalization to star networks is capable of detecting full network nonlocality in quantum theory. More generally, we point out that established methods for analyzing local and theoryindependent correlations in networks can be combined in order to systematically deduce sufficient conditions for full network nonlocality in any network and input-output scenario. We demonstrate the usefulness of these methods by constructing polynomial witnesses of full network nonlocality for the bilocal scenario. Then, we show that these inequalities can be violated via quantum elegant joint measurements.

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confidence: 99%

Full Network Nonlocality

2022

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“…As a tool for studying network entanglement, we use the inflation technique [17,32]. The basic idea is depicted FIG.…”

Section: Networkmentioning

confidence: 99%

“…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]. Still, the present results are limited to simple networks like the triangle network, noise-free networks or networks build from specific quantum states, or bounded to small dimensions due to numerical limitations.…”

Section: Introductionmentioning

confidence: 99%

Quantum Networks and Symmetries

Hansenne¹,

Kraft³

et al. 2021

Preprint

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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.

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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].…”

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confidence: 99%

“…First, it would be interesting to determine if either NLHS assemblages or the full set of network assemblages can be characterized via techniques based on semidefinite programming, using for instance the approach of Ref. [18]. A related direction is to further classify NLHS models based on the properties of the sources.…”

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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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Quantum Inflation: A General Approach to Quantum Causal Compatibility

Cited by 48 publications

References 54 publications

Full Network Nonlocality

Full Network Nonlocality

Quantum Networks and Symmetries

Network Quantum Steering

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