[Paper Review] Testing entanglement and Bell inequalities in $H o ZZ$

J. A. Aguilar–Saavedra, Amanda M Bernal+2 more|arXiv (Cornell University)|Sep 27, 2022

Quantum Mechanics and Applications4 citations

TL;DR

This paper proposes a novel framework to test quantum entanglement and Bell inequality violations in Higgs boson decays to two Z bosons, where each Z decays to light leptons. Using spin correlation observables derived from the H→ZZ decay, the authors derive necessary and sufficient conditions for entanglement and improved criteria for Bell inequality violation, showing that with 300 fb⁻¹ luminosity, entanglement can be detected above 3σ significance, and at HL-LHC (3 ab⁻¹), the significance exceeds 5σ for entanglement and reaches 4.5σ for Bell inequality violation.

ABSTRACT

We discuss quantum entanglement and violation of Bell inequalities in the $H ightarrow ZZ$ 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 $H o ZZ$ 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 $L = 300 ext{fb}^{-1}$ entanglement can be probed at $> 3σ$ level. For $L = 3 ext{ab}^{-1}$ (HL-LHC) entanglement can be probed beyond the $5σ$ level, while the sensitivity to a violation of the Bell inequalities is at the $4.5σ$ level

Motivation & Objective

• To develop a practical framework for extracting entanglement and Bell inequality violation information from H→ZZ decay data at high-energy colliders.
• To derive necessary and sufficient conditions for entanglement in the H→ZZ system using only two measurable parameters.
• To propose a new, improved Bell operator that provides a more sensitive test for Bell inequality violations than previous approaches.
• To assess the statistical sensitivity of future LHC data to probe quantum nonlocality in Higgs boson decays.
• To evaluate the feasibility of detecting entanglement and Bell inequality violations with realistic luminosity levels (300 fb⁻¹ and 3 ab⁻¹).

Proposed method

• Construct the spin density matrix ρ for the H→ZZ decay in a basis of Hermitian operators, with coefficients determined from experimental data.
• Apply the Peres-Horodecki criterion as a necessary and sufficient condition for entanglement in the H→ZZ system due to symmetry constraints.
• Derive a new Bell operator based on the CGLMP inequality for d=3 systems, optimized for maximally entangled states.
• Express the Bell operator in terms of unitary matrices, spin-1 projection operators, and cyclic permutation matrices to enable direct experimental evaluation.
• Use the expectation value of the Bell operator to compute the quantum violation of Bell inequalities.
• Perform a statistical analysis of the signal significance using Monte Carlo simulations with realistic luminosities (300 fb⁻¹ and 3 ab⁻¹).

Experimental results

Research questions

• RQ1 Can entanglement in the H→ZZ decay be detected with current and future LHC luminosities using spin correlation observables?
• RQ2 What are the necessary and sufficient conditions for entanglement in the H→ZZ system, expressible in terms of only two measurable parameters?
• RQ3 Can a new Bell operator provide a more sensitive test for Bell inequality violation than existing proposals in the context of H→ZZ decays?
• RQ4 What is the statistical significance of detecting entanglement and Bell inequality violation at the LHC and HL-LHC?
• RQ5 How does the quasi-maximal entanglement of the H→ZZ system enhance the feasibility of testing foundational quantum phenomena at high energies?

Key findings

• With a luminosity of 300 fb⁻¹, entanglement in the H→ZZ decay can be probed at a significance level exceeding 3σ.
• At the HL-LHC with 3 ab⁻¹ luminosity, the significance of entanglement detection exceeds 5σ, indicating a robust discovery potential.
• The violation of Bell inequalities can be probed at a significance level of 4.5σ with 3 ab⁻¹ luminosity, demonstrating high sensitivity to nonlocality.
• The authors derive a necessary and sufficient condition for entanglement in terms of only two measurable parameters, simplifying experimental analysis.
• The proposed Bell operator provides a more powerful and improved indicator for Bell inequality violation compared to previous approaches, especially for d=3 systems.
• The H→ZZ decay channel offers a clean, quasi-maximally entangled system, making it highly promising for testing foundational quantum phenomena at high energies despite low statistics.