Reexamination of the Kochen-Specker theorem: Relaxation of the completeness assumption

Onggadinata, Kelvin; Kaszlikowski, Dagomir; Kurzyński, Paweł

doi:10.1103/physreva.107.022223

Cited by 4 publications

(3 citation statements)

References 27 publications

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“…In their framework, there are quantum states whose only phase-space representations that respect the uncertainty bound involve negative probabilities. Onggadinata et al [15] derive the qubit with its full dynamics via an entropic invariance principle involving signed probabilities.…”

Section: Introductionmentioning

confidence: 99%

Agreement and disagreement in a non-classical world

Brandenburger,

Contreras-Tejada,

La Mura

et al. 2024

Phil. Trans. R. Soc. A.

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The Agreement Theorem Aumann (1976 Ann. Stat. 4 , 1236–1239. ( doi:10.1214/aos/1176343654 )) states that if two Bayesian agents start with a common prior, then they cannot have common knowledge that they hold different posterior probabilities of some underlying event of interest. In short, the two agents cannot ‘agree to disagree’. This result applies in the classical domain where classical probability theory applies. But in non-classical domains, such as the quantum world, classical probability theory does not apply. Inspired principally by their use in quantum mechanics, we employ signed probabilities to investigate the epistemics of the non-classical world. We find that here, too, it cannot be common knowledge that two agents assign different probabilities to an event of interest. However, in a non-classical domain, unlike the classical case, it can be common certainty that two agents assign different probabilities to an event of interest. Finally, in a non-classical domain, it cannot be common certainty that two agents assign different probabilities, if communication of their common certainty is possible—even if communication does not take place. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

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Section: Introductionmentioning

confidence: 99%

Agreement and disagreement in a non-classical world

Brandenburger,

Contreras-Tejada,

La Mura

et al. 2024

Phil. Trans. R. Soc. A.

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“…Most Bell-type inequalities for various classes of quantum networks are nonlinear due to the non-convexity of the multipartite correlation space [17][18][19]. In the simplest two-source quantum network, the linear and nonlinear bilocal inequalities are extensively studied [20][21][22][23][24][25]. Recently, Bell nonlocality in the star-shaped network [28][29][30][31][32][33][34] and other broader classes of quantum networks has also been widely studied [17,30,35,36].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal correlations in quantum networks distributed with different entangled states

Hsu

2024

New J. Phys.

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We initiate the study of the nonlocal correlations in generic asymmetric quantum networks in a star conﬁguration. Therein, the diverse unrelated sources can emit either partially or maximally entangled states, while the observers employ varying numbers of measurement settings. We propose nonlinear Bell inequalities tailored to the distributed entangled states. Speciﬁcally, we demonstrate that the algebraic maximal violations of the proposed nonlinear Bell inequalities are physically achievable within the quantum region. To achieve this, we construct the segmented Bell operators through the cut-graft-mix method applied to the Bell operators in the standard Bell tests. Furthermore, we devise the ﬁtting Bell operators using the sum-of-square approach.

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“…The idea of studying anomalous weak values from the perspective of anomalous quasi-probabilities has also appeared before in a less general description. From a rather broad view, negative joint quasi-probabilities are always capable of reproducing experimental data in quantum theory [27,28], but there are many such distributions capable of reproducing the strongest possible quantum correlations [29][30][31][32], a fact that somewhat disfavours those as good explanations due to fine-tuning arguments. Ref.…”

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confidence: 99%