Network configuration theory for all networks

Luo, Ming-Xing

doi:10.48550/arxiv.2107.05846

Cited by 3 publications

(4 citation statements)

References 47 publications

(203 reference statements)

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“…Reference [151] conjectures that the Finner inequalities hold for any network and any no-signalling theory. This conjecture is proved in reference [153], which also provides an explicit proof of the inequality p(a, b, c) p(a) 1− 1 m p(b)…”

Section: Limits From Finner Inequalitiesmentioning

confidence: 83%

Bell nonlocality in networks

et al. 2022

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Bell’s theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts predictions far beyond the traditional scenario of the Einstein-Podolsky-Rosen paradox. In the last decade, the investigation of nonlocality has moved beyond Bell’s theorem to consider more sophisticated experiments that involve several independent sources that distribute shares of physical systems among many parties in a network. Network scenarios, and the nonlocal correlations that they give rise to, lead to phenomena that have no counterpart in traditional Bell experiments, thus presenting a formidable conceptual and practical challenge. This review discusses the main concepts, methods, results and future challenges in the emerging topic of Bell nonlocality in networks.

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Section: Limits From Finner Inequalitiesmentioning

confidence: 83%

Bell nonlocality in networks

et al. 2022

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“…which cannot be generated from all networks in Figure 2a-c. [19][20][21] This yields to a further problem to distinguish different configurations of triangle networks. Here, we present an informational method as: [15]…”

Section: Results 2 For Any Joint Distribution On Finite Sample Spaces...mentioning

confidence: 99%

“…and its permutations using the second-order inflation method, [20] as shown in Figure 3, where a, b, c, d ≥ 0 and a…”

Section: Example 2 Consider a Mixture Of Ghz-type Distribution And Wt...mentioning

confidence: 99%

Negative Shannon Information Hides Networks

Luo

2022

Adv Quantum Tech

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Shannon information is defined for characterizing the uncertainty information of classical probabilistic distributions. As an uncertainty measure it is generally believed to be positive. This holds for any information quantity from two random variables because of the polymatroidal axioms. However, it is unknown why there is negative information for more than two random variables on finite dimensional spaces. It is first shown that the negative tripartite Shannon mutual information implies specific Bayesian network representations of its joint distribution. Then it is shown that the negative Shannon information is obtained from general tripartite Bayesian networks with quantum realizations. This provides a device‐independent witness of negative Shannon information. Finally the result is extended for general networks. The present result shows new insights in the network compatibility from non‐Shannon information inequalities.

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“…The power and limitations of such networks have already been studied in Refs. [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ], however, it is still unclear which useful quantum states can actually be prepared using them. In the most general definition, the parties and the sources can additionally share a global classical random variable, and we say that such networks arise from local operations and shared randomness ( losr ).…”

Section: Introductionmentioning

confidence: 99%

Covariance-Matrix-Based Criteria for Network Entanglement

Hansenne,

Gühne

2023

Entropy

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Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum sources and local operations are not yet well understood. Covariance matrices, which are powerful tools in entanglement theory, have been also applied to the network scenario. We present simple proofs for the decomposition of such matrices into the sum of positive semi-definite block matrices and, based on that, develop analytical and computable necessary criteria for preparing states in quantum networks. These criteria can be applied to networks where nodes share at most one source, such as all bipartite networks.

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Network configuration theory for all networks

Cited by 3 publications

References 47 publications

Bell nonlocality in networks

Bell nonlocality in networks

Negative Shannon Information Hides Networks

Covariance-Matrix-Based Criteria for Network Entanglement

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