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arXiv:2408.05010

Entanglement and Bell inequality violation in $B\to \it{ΦΦ}$ decays

Emidio Gabrielli A, Luca Marzola

Published Aug 9, 2024• 0 citations
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Abstract

The decays of the $B$ meson into vector mesons, observed at the LHCb experiment, provide an ideal laboratory to investigate particle physics phenomena with quantum information theory methods. In this article, we focus on the decays yielding a pair of $\itΦ$ mesons to investigate the presence of entanglement in the spin correlations of the system and quantify the amount of Bell inequality violation it entails. Our results show that the present LHCb data allows access to entanglement and to the Bell inequality violation with a significance exceeding the 5$σ$ threshold in both the cases. This demonstrates that the strong and electroweak interactions responsible for the $B$ meson decay act as a source of entanglement and the quantum mechanics nature of high-energy phenomena. Particular attention is paid to the assessment of loopholes: deficiencies in the experimental setup which could invalidate the results of the Bell test.

DOI
10.48550/arxiv.2408.05010

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Entanglement and Bell inequality violation in B→ΦΦB\to \it{ΦΦ}B→ΦΦ decays
The decays of the BBB meson into vector mesons, observed at the LHCb experiment, provide an ideal laboratory to investigate particle physics phenomena with quantum information theory methods. In this article, we focus on the decays yielding a pair of Φ\itΦΦ mesons to investigate the presence of entanglement in the spin correlations of the system and quantify the amount of Bell inequality violation it entails. Our results show that the present LHCb data allows access to entanglement and to the Bell inequality violation with a significance exceeding the 5σσσ threshold in both the cases. This demonstrates that the strong and electroweak interactions responsible for the BBB meson decay act as a source of entanglement and the quantum mechanics nature of high-energy phenomena. Particular attention is paid to the assessment of loopholes: deficiencies in the experimental setup which could invalidate the results of the Bell test.
The decays of the B meson into vector mesons, observed during the LHCb experiment, provide an ideal laboratory to investigate particle physics phenomena with quantum information theory methods. In this article, we focus on the decays yielding a pair of ϕ mesons to investigate the presence of entanglement in the spin correlations of the system and quantify the amount of Bell inequality violation it entails. Our results show that the present LHCb data allow access to entanglement and to the Bell inequality violation with a significance exceeding the 5σ threshold in both the cases. This demonstrates that the strong and electroweak interactions responsible for the B meson decay act as a source of entanglement and the quantum mechanics nature of high-energy phenomena. Particular attention is paid to the assessment of loopholes: deficiencies in the experimental setup which could invalidate the results of the Bell test.
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Bell inequality is violated in B0→J/ψ K⋆(892)0B^0\to J/ψ\, K^{\star}(892)^0B0→J/ψK⋆(892)0 decays
The violation of the Bell inequality is one of the hallmarks of quantum mechanics and can be used to rule out local deterministic alternative descriptions. We utilize the data analysis published by the LHCb collaboration on the helicity amplitudes for the decay B0→J/ψ K∗(892)0B^0\to J/ψ\,K^*(892)^0B0→J/ψK∗(892)0 to compute the entanglement among the polarizations of the final vector mesons and the violation of the Bell inequality that it entails. We find that quantum entanglement can be detected with a significance well above 5σσσ (nominally 84σσσ) and Bell inequality is violated with a significance well above 5σσσ (nominally 36σσσ) -- thereby firmly establishing these distinguishing feature of quantum mechanics at high energies in a collider setting and in the presence of strong and weak interactions. Entanglement is also present and the Bell inequality is violated in other decays of the BBB mesons into vector mesons, but with lesser significance.
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We discuss quantum entanglement and violation of Bell inequalities in the $H\ensuremath{\rightarrow}ZZ$ decay, in particular when the two ZZZ-bosons decay into light leptons. Although such process implies an important suppression of the statistics, this is traded by clean signals from a ``quasi maximally entangled'' system, which makes it very promising to check these crucial phenomena at high energy. In this paper we devise a novel framework to extract from $H\ensuremath{\rightarrow}ZZ$ data all significant information related to this goal, in particular spin correlation observables. In this context we derive sufficient and necessary conditions for entanglement in terms of only two parameters. Likewise, we obtain a sufficient and improved condition for the violation of Bell-type inequalities. The numerical analysis shows that with a luminosity of $L=300\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ entanglement can be probed at $>3\ensuremath{\sigma}$ level. For $L=3\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ (HL-LHC) entanglement can be probed beyond the $5\ensuremath{\sigma}$ level, while the sensitivity to a violation of the Bell inequalities is at the $4.5\ensuremath{\sigma}$ level.