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arXiv:2209.13441 · Physical review. D/Physical review. D.

Testing entanglement and Bell inequalities in H→ZZ

J. A. Aguilar–Saavedra, Alexander Bernal, J.A. Casas, Jesús M. Moreno

Published Jan 20, 2023• 91 citations
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Abstract

We discuss quantum entanglement and violation of Bell inequalities in the $H\ensuremath{\rightarrow}ZZ$ decay, in particular when the two $Z$-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.

DOI
10.1103/physrevd.107.016012

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Abstract Recent studies have shown that observing entangled particle states at a particle collider, such as the Large Hadron Collider (LHC), and testing the violation of Bell inequality in them can open up new research areas for studying high energy physics. We examine the presence of quantum entanglement in the process at leading order. We apply a generally recognized method, quantum state tomography, to reconstruct the spin density matrix of the joint ZZ system, through which all the relevant observables can be obtained. The angular distribution of the final leptons is obtained from simulated events using a Monte-Carlo program, which is used to reconstruct the spin density matrix. A non-zero value of the lower bound of the concurrence is measured with the simulated data. The numerical analysis shows that, with the luminosity corresponding to LHC Run 2+3, entanglement can be probed at the 2 level and up to the 3.75 level for High-Luminosity LHC data (3ab -1 ), revealing the possibility of finding quantum entanglement in real collider experiments.